Triangle Seminars
July 2010
Thu
1 Jul 2010
A New Look At The Path Integral of Quantum Mechanics
Edward Witten
(IAS)
June 2010
Mon
14 Jun 2010
Supersymmetry, Localization and Quantum Entropy Function
Ipsita Mandal
(Harish-Chandra)
Abstract:
AdS_2/CFT_1 correspondence leads to a prescription for computing the degeneracy of black hole states in terms of path integral over string fields living on the near horizon geometry of the black hole. In this talk, I will discuss about how to make use of the enhanced supersymmetries of the near horizon geometry and localization techniques to argue that the path integral receives contribution only from a special class of string field configurations which are invariant under a subgroup of the supersymmetry transformations. I will identify saddle points which are invariant under this subgroup. I will also use this analysis to show that the integration over infinite number of zero modes generated by the asymptotic symmetries of AdS_2 generate a finite contribution to the path integral.
AdS_2/CFT_1 correspondence leads to a prescription for computing the degeneracy of black hole states in terms of path integral over string fields living on the near horizon geometry of the black hole. In this talk, I will discuss about how to make use of the enhanced supersymmetries of the near horizon geometry and localization techniques to argue that the path integral receives contribution only from a special class of string field configurations which are invariant under a subgroup of the supersymmetry transformations. I will identify saddle points which are invariant under this subgroup. I will also use this analysis to show that the integration over infinite number of zero modes generated by the asymptotic symmetries of AdS_2 generate a finite contribution to the path integral.
Posted by: QMW
May 2010
Thu
27 May 2010
String Theory and Many-Body Physics
Djordje Minic
(Virginia Tech)
Abstract:
Recent theoretical advances in string theory relate
in an unexpected way the physics of gravity in certain D dimensional
space-times with the dynamics of quantum field theories living
on the associated (D-1) dimensional space-time boundary. This
unsuspected relationship offers a remarkable new tool
for dealing with some outstanding problems in condensed matter
physics. In the first part of the talk I aim to explain both the intuitive and
technical underpinnings of these new developments. In the second half of
the talk I will present some recent results on aging in systems far
from equilibrium and also some new avenues for
research in condensed matter physics which involve the interplay of gauge
fields, membranes and many-body systems .
In particular this last work opens up an
exciting possibility for fundamentally new states of condensed matter.
Recent theoretical advances in string theory relate
in an unexpected way the physics of gravity in certain D dimensional
space-times with the dynamics of quantum field theories living
on the associated (D-1) dimensional space-time boundary. This
unsuspected relationship offers a remarkable new tool
for dealing with some outstanding problems in condensed matter
physics. In the first part of the talk I aim to explain both the intuitive and
technical underpinnings of these new developments. In the second half of
the talk I will present some recent results on aging in systems far
from equilibrium and also some new avenues for
research in condensed matter physics which involve the interplay of gauge
fields, membranes and many-body systems .
In particular this last work opens up an
exciting possibility for fundamentally new states of condensed matter.
Posted by: QMW
Thu
20 May 2010
Counting Abelian Orbifolds
Amihay Hanany
(Imperial)
Abstract:
Brane Tilings give a large class of SCFT's in 3+1 and 2+1 dimensions.
In this talk I will discuss several attempts to classify all such models.
Special attention will be devoted to the class of Abelian orbifolds of C3 and of C4.
Statistical properties of these models can be derived using some techniques in crystallography and in number theory.
Brane Tilings give a large class of SCFT's in 3+1 and 2+1 dimensions.
In this talk I will discuss several attempts to classify all such models.
Special attention will be devoted to the class of Abelian orbifolds of C3 and of C4.
Statistical properties of these models can be derived using some techniques in crystallography and in number theory.
Posted by: QMW
Fri
14 May 2010
Non-Gaussianity as a Probe of Fundamental Physics
Yi Wang
(McGill)
Abstract:
Non-Gaussianity, which denotes the non-Gaussian feature of
the CMB temperature fluctuation, is potentially the most promising
probe of inflation. In this talk, we discuss some recent research
topics in this field, namely non-Gaussianity for DBI inflation,
quasi-single field inflation and multi-stream inflation. Special
attention is paid on the relation between non-Gaussianity and string
theory.
Non-Gaussianity, which denotes the non-Gaussian feature of
the CMB temperature fluctuation, is potentially the most promising
probe of inflation. In this talk, we discuss some recent research
topics in this field, namely non-Gaussianity for DBI inflation,
quasi-single field inflation and multi-stream inflation. Special
attention is paid on the relation between non-Gaussianity and string
theory.
Posted by: QMW
Thu
13 May 2010
Higher Derivative Gravity and AdS/CFT
Manuela Kulaxizi
(Amsterdam)
Abstract:
We will discuss a special class of higher derivative gravity theories called Lovelock gravities, in the context of holography. For a generic Lovelock gravity in arbitrary dimensions, we will formulate the existence condition for asymptotically AdS black holes. Then, causality of the dual finite temperature CFT will be shown to impose constraints on the Lovelock parameters. Calculation of the holographic Weyl anomaly in 6+1 dimensions reveals that these constraints are completely equivalent to the ones determined by requiring positivity of the energy flux. Implications of these results on the viscosity to entropy bound will also be discussed. This talk is based on hep-th/0910.5347, 0912.1877, 0912.4244.
We will discuss a special class of higher derivative gravity theories called Lovelock gravities, in the context of holography. For a generic Lovelock gravity in arbitrary dimensions, we will formulate the existence condition for asymptotically AdS black holes. Then, causality of the dual finite temperature CFT will be shown to impose constraints on the Lovelock parameters. Calculation of the holographic Weyl anomaly in 6+1 dimensions reveals that these constraints are completely equivalent to the ones determined by requiring positivity of the energy flux. Implications of these results on the viscosity to entropy bound will also be discussed. This talk is based on hep-th/0910.5347, 0912.1877, 0912.4244.
Posted by: QMW
April 2010
Thu
29 Apr 2010
SUSY Breaking in N=2 QFT
Matthew Buican
(CERN)
Abstract:
We will show that a large class of N=2 SUSY field theories do not have SUSY breaking vacua.
We will show that a large class of N=2 SUSY field theories do not have SUSY breaking vacua.
Posted by: QMW
Wed
28 Apr 2010
Prospects of the Heterotic String
Burt Ovrut
(University of Pennsylvania)
Abstract:
The current status of realistic particle physics models and cosmology in heterotic string theory, and their potential predictions for the LHC and cosmological observations, will be discussed.
The current status of realistic particle physics models and cosmology in heterotic string theory, and their potential predictions for the LHC and cosmological observations, will be discussed.
Posted by: IC
Tue
20 Apr 2010
Aspects of integrability in superconformal Chern-Simons theories
Joe Minahan
(Uppsala)
Abstract:
In this talk I will discuss the apparent integrability of large N ABJM models and the possible integrability of its ABJ extension. I will also discuss recent work to compute a coupling dependent function that explicitly appears in the magnon dispersion relations and Bethe equations for these models.
In this talk I will discuss the apparent integrability of large N ABJM models and the possible integrability of its ABJ extension. I will also discuss recent work to compute a coupling dependent function that explicitly appears in the magnon dispersion relations and Bethe equations for these models.
Posted by: QMW
Thu
15 Apr 2010
Covariant vertex operators for cosmic strings
Dimitri Skliros
(Sussex)
Abstract:
I will discuss the first construction of coherent states (and other
massive states with arbitrarily exited harmonics) in the covariant
formalism for both open and closed strings with applications to cosmic
strings in mind. Furthermore, I provide an explicit map that relates
three different descriptions of cosmic strings: classical strings,
lightcone gauge quantum states and covariant vertex operators,
highlighting the virtues and shortcomings of each. I will then go on to
discuss applications and future directions: string amplitude computations
with such vertices and in particular decays of (the phenomenologically
promising) cosmic strings with non-degenerate cusps in a framework that
naturally incorporates the effects of gravitational backreaction.
I will discuss the first construction of coherent states (and other
massive states with arbitrarily exited harmonics) in the covariant
formalism for both open and closed strings with applications to cosmic
strings in mind. Furthermore, I provide an explicit map that relates
three different descriptions of cosmic strings: classical strings,
lightcone gauge quantum states and covariant vertex operators,
highlighting the virtues and shortcomings of each. I will then go on to
discuss applications and future directions: string amplitude computations
with such vertices and in particular decays of (the phenomenologically
promising) cosmic strings with non-degenerate cusps in a framework that
naturally incorporates the effects of gravitational backreaction.
Posted by: QMW
Wed
14 Apr 2010
Holographic QCD
Nick Evans
(Southampton)
Abstract:
The D3/D7 system provides a simple holographic description of a strongly coupled gauge theory with quarks. By introducing a range of deformations of the AdS5 space a variety of familair phenomena in gauge theory can be investigated quantitatively. These include a running gauge coupling, temperature, chemical potential, and magnetic fields leading to confinement and chiral symmetry breaking, as well as bound mesons and their melting. I'll illustrate these phenomena with examples and derive the phase diagram of a chiral symmetry breaking theory. Finally I shall discuss how hadronization can be modelled in such set ups and propose that rho meson emission should be described by a simple EM radiation problem.
The D3/D7 system provides a simple holographic description of a strongly coupled gauge theory with quarks. By introducing a range of deformations of the AdS5 space a variety of familair phenomena in gauge theory can be investigated quantitatively. These include a running gauge coupling, temperature, chemical potential, and magnetic fields leading to confinement and chiral symmetry breaking, as well as bound mesons and their melting. I'll illustrate these phenomena with examples and derive the phase diagram of a chiral symmetry breaking theory. Finally I shall discuss how hadronization can be modelled in such set ups and propose that rho meson emission should be described by a simple EM radiation problem.
Posted by: QMW
Thu
8 Apr 2010
Genus two partition function of chiral conformal field theories
Roberto Volpato
(ETH Zurich)
Abstract:
The existence of a modular invariant genus two partition function
implies infinitely many relations among the structure constants of a
chiral self-dual conformal field theory. All of these relations can be
shown to be a consequence of the associativity of the OPE, as well as
the modular covariance properties of the torus one-point functions.
Using these techniques we prove that for the proposed extremal conformal
field theories at c=24k a consistent genus two vacuum amplitude exists
for all k, but that this does not actually check the consistency of
these theories beyond what is already testable at genus one.
The existence of a modular invariant genus two partition function
implies infinitely many relations among the structure constants of a
chiral self-dual conformal field theory. All of these relations can be
shown to be a consequence of the associativity of the OPE, as well as
the modular covariance properties of the torus one-point functions.
Using these techniques we prove that for the proposed extremal conformal
field theories at c=24k a consistent genus two vacuum amplitude exists
for all k, but that this does not actually check the consistency of
these theories beyond what is already testable at genus one.
Posted by: QMW
Thu
1 Apr 2010
Extremal black holes: a status report
Joan Simon
(Edinburgh)
Abstract:
I will review some recent attempts at providing a microscopic description
for extremal black holes. First, I will explain a constituent model for extremal non-rotating non-BPS asymptoticaly flat black holes. Second,
I will summarise the main claims in the so called extremal BH/CFT
correspondence, pointing out how a chiral CFT can emerge as a limit
of a non-chiral CFT. Finally, I will use R-charge AdS black holes
to derive the existence of emergent IR CFTs, similar to the ones
that have been argued to capture some interesting quantum criticality
phenomena in some strongly coupled condensed matter systems.
I will review some recent attempts at providing a microscopic description
for extremal black holes. First, I will explain a constituent model for extremal non-rotating non-BPS asymptoticaly flat black holes. Second,
I will summarise the main claims in the so called extremal BH/CFT
correspondence, pointing out how a chiral CFT can emerge as a limit
of a non-chiral CFT. Finally, I will use R-charge AdS black holes
to derive the existence of emergent IR CFTs, similar to the ones
that have been argued to capture some interesting quantum criticality
phenomena in some strongly coupled condensed matter systems.
Posted by: QMW
March 2010
Tue
30 Mar 2010
Evolutionary games on structured populations
Christoforos Hadjichrysanthou
(City University)
Abstract:
Evolutionary dynamics models have been mainly studied on homogeneous infinite populations. However, real populations are neither homogeneously mixed nor infinite. We investigate the stochastic evolutionary game dynamics on structured populations represented by graphs. We consider three simple graphs of finite number of vertices: the star, the circle and the complete graph. We present exact formulae for the fixation probability of a single mutant individual introduced into the graph and the speed of the evolutionary process, namely the mean time to absorption (either mutant fixation or extinction) and the mean time to mutant fixation. Through numerical examples we show the significant impact of the structure of the population, the population size and the payoff matrix on the above quantities.
Evolutionary dynamics models have been mainly studied on homogeneous infinite populations. However, real populations are neither homogeneously mixed nor infinite. We investigate the stochastic evolutionary game dynamics on structured populations represented by graphs. We consider three simple graphs of finite number of vertices: the star, the circle and the complete graph. We present exact formulae for the fixation probability of a single mutant individual introduced into the graph and the speed of the evolutionary process, namely the mean time to absorption (either mutant fixation or extinction) and the mean time to mutant fixation. Through numerical examples we show the significant impact of the structure of the population, the population size and the payoff matrix on the above quantities.
Posted by: KCL
Thu
25 Mar 2010
M2-branes at hypersurface singularities and their deformations
James Sparks
(Oxford)
Abstract:
I will introduce a family of supersymmetric Chern-Simons-matter theories in d=2+1 dimensions, labelled by a positive integer n, and argue using a number of different dual descriptions that these describe the worldvolume dynamics of M2-branes at a corresponding family of four-fold hypersurface singularities (the n=1 theory being the ABJM theory). The IR properties of these theories and their deformations are also studied.
I will introduce a family of supersymmetric Chern-Simons-matter theories in d=2+1 dimensions, labelled by a positive integer n, and argue using a number of different dual descriptions that these describe the worldvolume dynamics of M2-branes at a corresponding family of four-fold hypersurface singularities (the n=1 theory being the ABJM theory). The IR properties of these theories and their deformations are also studied.
Posted by: QMW
Wed
24 Mar 2010
Extremal black holes: a status report
Joan Simon
(Edinburgh)
Abstract:
I will review some recent attempts at providing a microscopic description
for extremal black holes. First, I will explain a constituent model for extremal non-rotating non-BPS asymptoticaly flat black holes. Second, I will summarise the main claims in the so called extremal BH/CFT correspondence, pointing out how a chiral CFT can emerge as a limit of a non-chiral CFT. Finally, I will use R-charge AdS black holes to derive the existence of emergent IR CFTs, similar to the ones that have been argued to capture some interesting quantum criticality phenomena in some strongly coupled condensed matter systems.
I will review some recent attempts at providing a microscopic description
for extremal black holes. First, I will explain a constituent model for extremal non-rotating non-BPS asymptoticaly flat black holes. Second, I will summarise the main claims in the so called extremal BH/CFT correspondence, pointing out how a chiral CFT can emerge as a limit of a non-chiral CFT. Finally, I will use R-charge AdS black holes to derive the existence of emergent IR CFTs, similar to the ones that have been argued to capture some interesting quantum criticality phenomena in some strongly coupled condensed matter systems.
Posted by: IC
Wed
17 Mar 2010
Quiver gauge theories from open topological string theory
📍 London
Nils Carqueville
(Munich)
Abstract:
Effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities can be studied from many points of view. In this talk we adopt a first principle approach via open topological string theory, which means that we construct the natural A-
infinity-structure of open string amplitudes in the associated D-brane category. This precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, one obtains a general and simple formula for effective superpotentials.
Effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities can be studied from many points of view. In this talk we adopt a first principle approach via open topological string theory, which means that we construct the natural A-
infinity-structure of open string amplitudes in the associated D-brane category. This precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, one obtains a general and simple formula for effective superpotentials.
Posted by: KCL
Tue
16 Mar 2010
A Geometric Apercu on N=1 Gauge Theories
Yang-Hui He
(Oxford University)
Abstract:
We present some new perspectives on N=1 gauge theories, especially SQCD, D-Brane Quiver Theories and the MSSM, from the stand-point of recent advances in computational and algorithmic algebraic geometry and commutative algebra. We introduce the plethystic program which systematically count gauge invariants and encodes certain hidden symmetries. Moreover, we discuss special structures of the vacuum moduli space, such as that of SQCD being Calabi-Yau.
We present some new perspectives on N=1 gauge theories, especially SQCD, D-Brane Quiver Theories and the MSSM, from the stand-point of recent advances in computational and algorithmic algebraic geometry and commutative algebra. We introduce the plethystic program which systematically count gauge invariants and encodes certain hidden symmetries. Moreover, we discuss special structures of the vacuum moduli space, such as that of SQCD being Calabi-Yau.
Posted by: KCL
Thu
11 Mar 2010
Pair production of small black holes in heterotic string theories
Massimo Bianchi
(Rome Tor Vergata)
Abstract:
After reviewing how small BPS black holes with two charges
can be described in perturbative Heterotic strings, we compute the
cross section for their pair production at tree level and analyze
angular and energy distributions. We consider both toroidal
compactifications and FHSV orbifold model, and comment on scenari with
large extra dimensions. Finally we briefly discuss how to extend our
results to non-BPS, non-extremal and rotating BH's.
After reviewing how small BPS black holes with two charges
can be described in perturbative Heterotic strings, we compute the
cross section for their pair production at tree level and analyze
angular and energy distributions. We consider both toroidal
compactifications and FHSV orbifold model, and comment on scenari with
large extra dimensions. Finally we briefly discuss how to extend our
results to non-BPS, non-extremal and rotating BH's.
Posted by: QMW
Wed
10 Mar 2010
Integrable nonlinear PDEs: recent progress and open questions
📍 London
Thanasis Fokas
(DAMTP)
Tue
9 Mar 2010
Superconductors and Quantum-Critical M-Theory
Julian Sonner
(Imperial College)
Abstract:
The Renormalisation Group tells us that, quite generically, quantum and classical many-body systems exhibit interesting scaling behaviour near critical points. Quantum critical points form a subset of these, corresponding to zero-temperature phase transitions. In the last decade, the AdS/CFT correspondence between conformal field theories on one side and string or M-Theory on the other side has developed into a rich and exciting subject. Until recently the applications of this 'duality' were mostly focused on theories relevant to model quantum field theories that are considered interesting from the point of view of high-energy particle physics - the prime example being N=4 SYM in d=4. In this talk I will describe how similar methods can be fruitfully applied to the theory of quantum critical phenomena in 2+1 dimensions. These systems are of practical interest, as it has been proposed that a quantum critical point underlies the strange behaviour of high-TC superconductors falling into the copper-oxide group.
The Renormalisation Group tells us that, quite generically, quantum and classical many-body systems exhibit interesting scaling behaviour near critical points. Quantum critical points form a subset of these, corresponding to zero-temperature phase transitions. In the last decade, the AdS/CFT correspondence between conformal field theories on one side and string or M-Theory on the other side has developed into a rich and exciting subject. Until recently the applications of this 'duality' were mostly focused on theories relevant to model quantum field theories that are considered interesting from the point of view of high-energy particle physics - the prime example being N=4 SYM in d=4. In this talk I will describe how similar methods can be fruitfully applied to the theory of quantum critical phenomena in 2+1 dimensions. These systems are of practical interest, as it has been proposed that a quantum critical point underlies the strange behaviour of high-TC superconductors falling into the copper-oxide group.
Posted by: KCL
Tue
9 Mar 2010
3d N=2 CFTs with chiral flavours from M2-branes at toric CY4 singularities
Stefano Cremonesi
(Tel Aviv)
Abstract:
Following the work of Aharony, Bergman, Jafferis and Maldacena, a great effort has been made to understand the 3d conformal gauge theories describing M2-branes at conical singularities. Special attention has been directed to N=2 supersymmetric AdS4/CFT3 pairs arising from M2-branes at toric CY 4-folds, where powerful algebraic techniques are available. After reviewing some results concerning brane tilings, the relation between the toric CY3 and CY4 moduli spaces of 4d and 3d toric quiver gauge theories, and M-theory/type IIA duality, I will explain how flavours naturally arise in this framework, and how their matter content and superpotential couplings to bifundamental fields are encoded in geometric data. Quantum effects are crucial in computing the moduli spaces of such flavoured quiver gauge theories. Any quiver Chern-Simons (CS) theory of the kind considered in the AdS4/CFT3 literature so far can be obtained by coupling a 3d gauge theory with the same quiver diagram but no CS terms to chiral flavours, and integrating them out via a real mass term.
Following the work of Aharony, Bergman, Jafferis and Maldacena, a great effort has been made to understand the 3d conformal gauge theories describing M2-branes at conical singularities. Special attention has been directed to N=2 supersymmetric AdS4/CFT3 pairs arising from M2-branes at toric CY 4-folds, where powerful algebraic techniques are available. After reviewing some results concerning brane tilings, the relation between the toric CY3 and CY4 moduli spaces of 4d and 3d toric quiver gauge theories, and M-theory/type IIA duality, I will explain how flavours naturally arise in this framework, and how their matter content and superpotential couplings to bifundamental fields are encoded in geometric data. Quantum effects are crucial in computing the moduli spaces of such flavoured quiver gauge theories. Any quiver Chern-Simons (CS) theory of the kind considered in the AdS4/CFT3 literature so far can be obtained by coupling a 3d gauge theory with the same quiver diagram but no CS terms to chiral flavours, and integrating them out via a real mass term.
Posted by: QMW
Thu
4 Mar 2010
Random Matrices and the Riemann zeta-function
Jon Keating
(Bristol)
Abstract:
The Riemann zeta-function, which encodes information about the primes, is the subject of one of the most important problems in mathematics: the Riemann Hypothesis. In the past few years connections have emerged with random matrix theory/matrix models. I shall review these connections.
The Riemann zeta-function, which encodes information about the primes, is the subject of one of the most important problems in mathematics: the Riemann Hypothesis. In the past few years connections have emerged with random matrix theory/matrix models. I shall review these connections.
Posted by: QMW
Wed
3 Mar 2010
On the universality classes of Strongly Coupled Doped systems
Elias Kiritsis
(Crete)
Abstract:
Effective Holographic Theories are employed in order to classify
and study the critical dynamics at low temperature of quantum field
theoritec systems in 2 and 3 spacial dimensions at finite charge density.
The relevant dynamics variables involve the energy momentum tensor, a scalar
relevant or marginal operator and the charge density current.
A wealth of scaling phases are found with interesting and sometimes
counterintuitive properties.
Effective Holographic Theories are employed in order to classify
and study the critical dynamics at low temperature of quantum field
theoritec systems in 2 and 3 spacial dimensions at finite charge density.
The relevant dynamics variables involve the energy momentum tensor, a scalar
relevant or marginal operator and the charge density current.
A wealth of scaling phases are found with interesting and sometimes
counterintuitive properties.
Posted by: IC
Wed
3 Mar 2010
Effective Strings and Emergent Gravity
Erik Verlinde
(University of Amsterdam)
Abstract:
I present arguments that suggest that string theory should be viewed as an effective framework just like quantum field theory. The open/closed string and UV/IR correspondence indicate that gravity is emergent. I introduce the concept of entropic force and discuss it's subtleties. Next I present the case for the entropic origin of gravity and outline a route toward its derivation. Finally, I discuss some of the possible implications on this new view on gravity.
I present arguments that suggest that string theory should be viewed as an effective framework just like quantum field theory. The open/closed string and UV/IR correspondence indicate that gravity is emergent. I introduce the concept of entropic force and discuss it's subtleties. Next I present the case for the entropic origin of gravity and outline a route toward its derivation. Finally, I discuss some of the possible implications on this new view on gravity.
Posted by: QMW
Tue
2 Mar 2010
2-vector spaces: an introduction to higher-dimensional category theory
Eugenia Cheung
(Sheffield University)
Abstract:
Category theory is used to study structures in various branches of mathematics, and higher-dimensional category theory is being developed to study higher-dimensional versions of those structures. Examples include higher homotopy theory, higher stacks and gerbes, extended topological quantum field theories, concurrency, type theory, and higher-dimensional representation theory. In this talk we will present two general methods for categorifying things, that is, for adding extra dimensions: enrichment and internalisation. We will show how these have been applied to the definition and study of 2-vector spaces, with 2-representation theory in mind. This talk will be introductory. In particular, it should not be necessary to be familiar with any category theory, although it will of course help
Category theory is used to study structures in various branches of mathematics, and higher-dimensional category theory is being developed to study higher-dimensional versions of those structures. Examples include higher homotopy theory, higher stacks and gerbes, extended topological quantum field theories, concurrency, type theory, and higher-dimensional representation theory. In this talk we will present two general methods for categorifying things, that is, for adding extra dimensions: enrichment and internalisation. We will show how these have been applied to the definition and study of 2-vector spaces, with 2-representation theory in mind. This talk will be introductory. In particular, it should not be necessary to be familiar with any category theory, although it will of course help
Posted by: KCL
February 2010
Thu
25 Feb 2010
Instabilities and new phases of higher dimensional vacuum rotating black holes
Pau Figueras
(Durham)
Abstract:
In this talk I will first review the recent progress made towards
finding instabilities of rotating vacuum black holes in higher
dimensions. I will show that singly spinning Myers-Perry black holes
exhibit an infinite sequence of zero modes that should connect them to
other black hole phases such as black rings and black saturns. In the
second part of my talk I will describe the gravitational instabilities
of Myers-Perry black holes with all the angular momenta equal. The
onset of instability is associated with the appearance of
time-independent perturbations which generically break all but one of
the rotational symmetries. In nine spacetime dimensions, this is
interpreted as evidence for the existence of a new 70-parameter family
of black hole solutions with only a single rotational symmetry.
In this talk I will first review the recent progress made towards
finding instabilities of rotating vacuum black holes in higher
dimensions. I will show that singly spinning Myers-Perry black holes
exhibit an infinite sequence of zero modes that should connect them to
other black hole phases such as black rings and black saturns. In the
second part of my talk I will describe the gravitational instabilities
of Myers-Perry black holes with all the angular momenta equal. The
onset of instability is associated with the appearance of
time-independent perturbations which generically break all but one of
the rotational symmetries. In nine spacetime dimensions, this is
interpreted as evidence for the existence of a new 70-parameter family
of black hole solutions with only a single rotational symmetry.
Posted by: QMW
Wed
24 Feb 2010
N=2 superconformal theories, M5 branes and (p,q)-webs
📍 London
Sergio Benvenuti
(Imperial)
Abstract:
In 2009 there has been progress in understanding and classifying the set of four dimensional field theories with N=2 SUSY. These models arise as M5 branes wrapped over a Riemann surface. We review this construction and describe a five dimensional point of view, using (p,q)-webs of 5branes in Type IIB string theory. This point of view makes many properties of the theories explicit. We will also touch on the AGT correspondence, that associates a 2-dimensional CFT, similar to the Liouville CFT, to the protected sector of four dimensional N=2 models.
In 2009 there has been progress in understanding and classifying the set of four dimensional field theories with N=2 SUSY. These models arise as M5 branes wrapped over a Riemann surface. We review this construction and describe a five dimensional point of view, using (p,q)-webs of 5branes in Type IIB string theory. This point of view makes many properties of the theories explicit. We will also touch on the AGT correspondence, that associates a 2-dimensional CFT, similar to the Liouville CFT, to the protected sector of four dimensional N=2 models.
Posted by: KCL
Wed
24 Feb 2010
Inching Towards Strange Metallic Holography
David Tong
(DAMTP, Cambridge)
Abstract:
Strange metals are materials with numerous anomalous properties.
The flow of electricity cannot be explained in the familiar language of a
fluid of individual electrons, but instead requires a new strongly
interacting description. In this talk, I will review some basic facts
about these materials. With this as motivation, I will explain how to
compute conductivity in certain strongly interacting, non-relativistic
field theories which are defined holographically.
Strange metals are materials with numerous anomalous properties.
The flow of electricity cannot be explained in the familiar language of a
fluid of individual electrons, but instead requires a new strongly
interacting description. In this talk, I will review some basic facts
about these materials. With this as motivation, I will explain how to
compute conductivity in certain strongly interacting, non-relativistic
field theories which are defined holographically.
Posted by: IC
Tue
23 Feb 2010
Matrix models, 2d CFTs and 4d N=2 gauge theories
Niclas Wyllard
(Chalmers University)
Abstract:
We review the recently uncovered connections between three classes of theories: A_r quiver matrix models, d=2 conformal A_r Toda field theories and d=4 N=2 conformal A_r quiver gauge theories
We review the recently uncovered connections between three classes of theories: A_r quiver matrix models, d=2 conformal A_r Toda field theories and d=4 N=2 conformal A_r quiver gauge theories
Posted by: KCL
Thu
18 Feb 2010
Solitons in Holographic Superfluids
Sean Nowling
(Helsinki)
Abstract:
The gauge/gravity duality provides a new set of tools for exploring
the physics near 2+1 dimensional quantum critical points. In many
highly quantum states of matter, soliton configurations yield clues
about the physics of both large and small length scales. I will
review a holographic model for a relativistic superfluid. I will then
discuss dark soliton and vortex solutions supported by this
superfluid.
The gauge/gravity duality provides a new set of tools for exploring
the physics near 2+1 dimensional quantum critical points. In many
highly quantum states of matter, soliton configurations yield clues
about the physics of both large and small length scales. I will
review a holographic model for a relativistic superfluid. I will then
discuss dark soliton and vortex solutions supported by this
superfluid.
Posted by: QMW
Wed
17 Feb 2010
Causality and Photon Propagation in Curved Spacetime
📍 London
Graham Shore
(Swansea )
Abstract:
We discuss the effect of vacuum polarization on the propagation of photons in curved spacetime in QED. A compact formula is presented for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit. This shows explicitly how the superluminal propagation found in the low-energy effective action is reconciled with causality.
The geometry of null geodesic congruences is found to imply
a novel analytic structure for the refractive index and
Green functions of QED in curved spacetime, which preserves
their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The Kramers-Kronig dispersion relation and the optical theorem for QFT in curved spacetime are discussed critically. The significance of the Penrose limit for black hole spacetimes and their relation to homogeneous plane waves is explained and unexpected features of light propagation in a number of spacetimes are described.
We discuss the effect of vacuum polarization on the propagation of photons in curved spacetime in QED. A compact formula is presented for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit. This shows explicitly how the superluminal propagation found in the low-energy effective action is reconciled with causality.
The geometry of null geodesic congruences is found to imply
a novel analytic structure for the refractive index and
Green functions of QED in curved spacetime, which preserves
their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The Kramers-Kronig dispersion relation and the optical theorem for QFT in curved spacetime are discussed critically. The significance of the Penrose limit for black hole spacetimes and their relation to homogeneous plane waves is explained and unexpected features of light propagation in a number of spacetimes are described.
Posted by: KCL
Wed
17 Feb 2010
Gradient formula for the beta function of 2d quantum field theory
Anatoly Konechny
(Heriot-Watt)
Abstract:
I will explain a gradient formula for beta functions of two-dimensional
quantum field theories. The gradient formula has the form derivative c = - (gij+Delta gij+bij) bj where bj are the beta functions, c and gij are the Zamolodchikov c-function and metric, bij is an antisymmetric tensor introduced by H. Osborn and Delta gij is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.
I will explain a gradient formula for beta functions of two-dimensional
quantum field theories. The gradient formula has the form derivative c = - (gij+Delta gij+bij) bj where bj are the beta functions, c and gij are the Zamolodchikov c-function and metric, bij is an antisymmetric tensor introduced by H. Osborn and Delta gij is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.
Posted by: IC
Tue
16 Feb 2010
Models of evolution on structured populations
Mark Broom
(City University)
Abstract:
We investigate two examples of models of populations with structure. These are different in character, with the common theme that the structure has an important influence on population outcomes. In the first part we consider a model of kleptoparasitism, the stealing of food from one animal by another. We investigate a model where individuals are allowed to fight in groups of more than two, as often occurs in real populations, but which has not featured in previous theoretical models. We find the equilibrium distribution of the population amongst various behavioural states, conditional upon the strategies played and environmental parameters, and then find evolutionarily stable strategies (ESSs) for the challenging behaviour of the participants. We show that ESSs can only come from a restricted subset of the possible strategies and that there is always at least one ESS. We show that there can be multiple ESSs, and indeed that the number of ESSs is unbounded. Finally we discuss the biological circumstances when particular ESSs occur in terms of key parameters such as the availability of food and the cost of fighting. The second part of the talk concerns the study of evolutionary dynamics on populations with some non-homogeneous structure, a topic in which there is a rapidly growing interest. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. This process is a Markov chain and we prove several mathematical results. For example we prove that for all but a restricted set of graphs, (almost) all states are accessible from the possible initial states. We then consider graphs within this restricted set or with considerable symmetry. To find the fixation probability of a line graph we relate this to a two-dimensional random walk which is not spatially homogeneous. We investigate our solutions numerically and find that for mutants with fitness greater than the resident, the existence of population structure helps the spread of the mutants. Thus it may be that models assuming well-mixed populations consistently underestimate the rate of evolutionary change.
We investigate two examples of models of populations with structure. These are different in character, with the common theme that the structure has an important influence on population outcomes. In the first part we consider a model of kleptoparasitism, the stealing of food from one animal by another. We investigate a model where individuals are allowed to fight in groups of more than two, as often occurs in real populations, but which has not featured in previous theoretical models. We find the equilibrium distribution of the population amongst various behavioural states, conditional upon the strategies played and environmental parameters, and then find evolutionarily stable strategies (ESSs) for the challenging behaviour of the participants. We show that ESSs can only come from a restricted subset of the possible strategies and that there is always at least one ESS. We show that there can be multiple ESSs, and indeed that the number of ESSs is unbounded. Finally we discuss the biological circumstances when particular ESSs occur in terms of key parameters such as the availability of food and the cost of fighting. The second part of the talk concerns the study of evolutionary dynamics on populations with some non-homogeneous structure, a topic in which there is a rapidly growing interest. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. This process is a Markov chain and we prove several mathematical results. For example we prove that for all but a restricted set of graphs, (almost) all states are accessible from the possible initial states. We then consider graphs within this restricted set or with considerable symmetry. To find the fixation probability of a line graph we relate this to a two-dimensional random walk which is not spatially homogeneous. We investigate our solutions numerically and find that for mutants with fitness greater than the resident, the existence of population structure helps the spread of the mutants. Thus it may be that models assuming well-mixed populations consistently underestimate the rate of evolutionary change.
Posted by: KCL
Wed
10 Feb 2010
tba
Atish Dabholkar
(Paris)
Abstract:
I will report on some recent progress on defining and computing finite
size effects in the entropy of black holes with highly nontrivial
agreements between thermodynamics and statistical mechanics. I will
describe a number of puzzles and their resolutions along with some exact
computations, and then briefly discuss the role of mock modular forms
and Borcherds-Kac-Moody superalgebras in this context.
I will report on some recent progress on defining and computing finite
size effects in the entropy of black holes with highly nontrivial
agreements between thermodynamics and statistical mechanics. I will
describe a number of puzzles and their resolutions along with some exact
computations, and then briefly discuss the role of mock modular forms
and Borcherds-Kac-Moody superalgebras in this context.
Posted by: KCL
Wed
10 Feb 2010
tba
Atish Dabholkar
(Paris)
Wed
10 Feb 2010
Massive 3D supergravities
Paul Townsend
(DAMTP, Cambridge)
Abstract:
Non-zero mass is compatible with unbroken gauge invariance in
three spacetime dimensions (3D). A systematic procedure for the
construction of massive gauge theories will be illustrated by new massive
gravity, which propagates unitarily two massive spin 2 modes in a
Minkowski vacuum. The supergravity extension of this model will be
presented along with new results on supersymmetric AdS vacua. The extension to a new N=8 3D supergravity will be discussed, as will be the AdS3CFT2 correspondence and possible connections to string/M-theory.
Non-zero mass is compatible with unbroken gauge invariance in
three spacetime dimensions (3D). A systematic procedure for the
construction of massive gauge theories will be illustrated by new massive
gravity, which propagates unitarily two massive spin 2 modes in a
Minkowski vacuum. The supergravity extension of this model will be
presented along with new results on supersymmetric AdS vacua. The extension to a new N=8 3D supergravity will be discussed, as will be the AdS3CFT2 correspondence and possible connections to string/M-theory.
Posted by: IC
Tue
9 Feb 2010
Knot invariants, knot homology and geometric representation theory
Geordie Williams
(Oxford University)
Abstract:
I will start by giving an introduction to polynomial knot invariants, as well as to Khovanov's more recent idea of knot homology. The goal is to find bi- and tri-graded vector spaces whose graded Euler characteristics are classical polynomial knot invariants (like the Jones or HOMFLYPT polynomial). I will then explain how HOMFLYPT homology can be given a transparent construction using some heavy machinery from geometric representation theory. This gives a bridge between link homology and techniques which have been developed for studying the characters of finite groups of Lie type.
I will start by giving an introduction to polynomial knot invariants, as well as to Khovanov's more recent idea of knot homology. The goal is to find bi- and tri-graded vector spaces whose graded Euler characteristics are classical polynomial knot invariants (like the Jones or HOMFLYPT polynomial). I will then explain how HOMFLYPT homology can be given a transparent construction using some heavy machinery from geometric representation theory. This gives a bridge between link homology and techniques which have been developed for studying the characters of finite groups of Lie type.
Posted by: KCL
Thu
4 Feb 2010
What is a Gerbe?
David Berman
(Queen Mary)
Abstract:
This is an introduction to Gerbes aimed at physicists. The approach will be to introduce Cech cohmology and its relation to gauge theories, monopoles and Wilson loops and then give the extension to extend these ideas to the relation between higher order Cech cohomolgy, gerbes and strings.
This is an introduction to Gerbes aimed at physicists. The approach will be to introduce Cech cohmology and its relation to gauge theories, monopoles and Wilson loops and then give the extension to extend these ideas to the relation between higher order Cech cohomolgy, gerbes and strings.
Posted by: QMW
Thu
4 Feb 2010
A supermatrix model for super-Chern-Simons-Matter
Nadav Drukker
(Humboldt)
Abstract:
I will present the 1/2 BPS Wilson loop operator of N=6 super Chern-
Simons-matter (ABJM theory) which is dual to the simplest macroscopic
open string in AdS4 x CP3. The Wilson loop couples, in addition to
the gauge and scalar fields of the theory, also to the fermions in the
bi-fundamental representation of the U(N) x U(M) gauge group. These
ingredients are naturally combined into a superconnection whose
holonomy gives the Wilson loop, which can be defined for any
representation of the supergroup U(NlM). Using the localization
calculation of Kapustin et al. I will then show that the circular loop
is computed by a supermatrix model and discuss the connection to pure
Chern-Simons theory with supergroup U(NlM).
I will present the 1/2 BPS Wilson loop operator of N=6 super Chern-
Simons-matter (ABJM theory) which is dual to the simplest macroscopic
open string in AdS4 x CP3. The Wilson loop couples, in addition to
the gauge and scalar fields of the theory, also to the fermions in the
bi-fundamental representation of the U(N) x U(M) gauge group. These
ingredients are naturally combined into a superconnection whose
holonomy gives the Wilson loop, which can be defined for any
representation of the supergroup U(NlM). Using the localization
calculation of Kapustin et al. I will then show that the circular loop
is computed by a supermatrix model and discuss the connection to pure
Chern-Simons theory with supergroup U(NlM).
Posted by: IC
Thu
4 Feb 2010
A matrix model for the topological string: Deriving the BKMP conjecture
Amir-Kian Kashani-Poor
(ENS, Paris)
Abstract:
In this talk, I will discuss work in progress with Bertrand Eynard, in
which we derive the BKMP remodelling the B-model conjecture, in the
large radius limit. This is the claim that Gromov-Witten invariants of any
toric Calabi-Yau 3-fold coincide with the spectral invariants of the
mirror curve. Our method consists in explicitly constructing a matrix
model which reproduces the topological string partition function obtained
via the vertex formalism, and then demonstrating that the spectral curve
of this matrix model coincides with the mirror geometry.
In this talk, I will discuss work in progress with Bertrand Eynard, in
which we derive the BKMP remodelling the B-model conjecture, in the
large radius limit. This is the claim that Gromov-Witten invariants of any
toric Calabi-Yau 3-fold coincide with the spectral invariants of the
mirror curve. Our method consists in explicitly constructing a matrix
model which reproduces the topological string partition function obtained
via the vertex formalism, and then demonstrating that the spectral curve
of this matrix model coincides with the mirror geometry.
Posted by: QMW
Wed
3 Feb 2010
Connections between U(N)xU(N) and SU(N)xSU(N) Membrane Theories
📍 London
Costis Papageorgakis
(KCL)
Abstract:
We will discuss how by integrating out a global U(1)B gauge field, the U(n)xU(n) ABJM models at level k are equivalent to SU(n)xSU(n) N=6 Chern-Simons theories with a Zk identification on the fields and a modified flux quantisation condition, but only when n and k are relatively prime. As a consequence, the ABJM model for two M2-branes in R8 can be identified with the N=8 SU(2)xSU(2) theory at k=1. We will also argue that the original N=8 SO(4)-theory of Bagger and Lambert, without modified flux quantisation, is equivalent to the U(2)xU(2) ABJM model at k=2 and hence describes the IR fixed point of a maximally supersymmetric three-dimensional O(4) gauge theory obtained in M-theory by an R8/Z2 orbifold without torsion.
We will discuss how by integrating out a global U(1)B gauge field, the U(n)xU(n) ABJM models at level k are equivalent to SU(n)xSU(n) N=6 Chern-Simons theories with a Zk identification on the fields and a modified flux quantisation condition, but only when n and k are relatively prime. As a consequence, the ABJM model for two M2-branes in R8 can be identified with the N=8 SU(2)xSU(2) theory at k=1. We will also argue that the original N=8 SO(4)-theory of Bagger and Lambert, without modified flux quantisation, is equivalent to the U(2)xU(2) ABJM model at k=2 and hence describes the IR fixed point of a maximally supersymmetric three-dimensional O(4) gauge theory obtained in M-theory by an R8/Z2 orbifold without torsion.
Posted by: KCL
Wed
3 Feb 2010
Viscosity and conductivity in general theories of gravity
Miguel Paulos
(DAMTP, Cambridge)
Abstract:
Recently there has been great interest in calculating transport coefficients
for field theories at large coupling, using AdS/CFT. In this talk I will
discuss recent work showing how to use the membrane paradigm to easily
compute the shear viscosity and conductivity in arbitrary gravity theories.
In a certain sense these can be thought of as effective couplings at the
black hole horizon dual to the field theory plasma. An explicit Wald-like
formula for these couplings is given for a large class of generalized
gravity theories.
Recently there has been great interest in calculating transport coefficients
for field theories at large coupling, using AdS/CFT. In this talk I will
discuss recent work showing how to use the membrane paradigm to easily
compute the shear viscosity and conductivity in arbitrary gravity theories.
In a certain sense these can be thought of as effective couplings at the
black hole horizon dual to the field theory plasma. An explicit Wald-like
formula for these couplings is given for a large class of generalized
gravity theories.
Posted by: IC
Tue
2 Feb 2010
Dimers and Calabi-Yaus
Alastair King
(University of Bath)
Abstract:
I will explain how a novel use of dimer models in string theory sheds light on the non-commutative geometry of toric Calabi-Yau 3-fold singularities (and also explain what this means).
I will explain how a novel use of dimer models in string theory sheds light on the non-commutative geometry of toric Calabi-Yau 3-fold singularities (and also explain what this means).
Posted by: KCL
January 2010
Fri
29 Jan 2010
Two topics in Chern-Simons/M2-brane duality
Nakwoo Kim
(University of Seoul)
Abstract:
We discuss a couple of topics motivated by the Chern-Simons type gauge theory description of M2-branes in nontrivial backgrounds. In the first part we start by briefly reviewing the 3-algebra construction of Bagger, Lambert and Gustavsson. Then we propose an orbifold truncation prescription of 3-algebra, and show how one can 'derive' the ABJM model through matrix regularization. In the second part, we report on some explicit classical solutions of rotating membranes in Sasaki-Einstein 7-manifold M(111). We discuss the dual operators on the CS side, for several different class of spinning membranes.
We discuss a couple of topics motivated by the Chern-Simons type gauge theory description of M2-branes in nontrivial backgrounds. In the first part we start by briefly reviewing the 3-algebra construction of Bagger, Lambert and Gustavsson. Then we propose an orbifold truncation prescription of 3-algebra, and show how one can 'derive' the ABJM model through matrix regularization. In the second part, we report on some explicit classical solutions of rotating membranes in Sasaki-Einstein 7-manifold M(111). We discuss the dual operators on the CS side, for several different class of spinning membranes.
Posted by: IC
Thu
28 Jan 2010
Leading singularities, twistor-strings and grassmannians
Lionel Mason
(Oxford)
Abstract:
Leading singularities are invariants of multi-loop scattering amplitudes (the full amplitude at tree level) obtained by generalized unitarity. In this talk we show how to construct multi-loop leading singularities on twistor space for maximally super-symmetric Yang-Mills (and gravity). Building on the tree-level twistor-string representation of scattering amplitudes, they can be represented as integrals over a moduli space of nodal curves in twistor space. We discuss how this might arise from a conjectural twistor-string path integral representation for the full loop amplitude. We also show how the construction relates to the Grassmannian representation of leading singularities conjectured by Arkani-Hamed et. al.. This shows firstly that all leading singularities can be represented in the Grassmannian, and secondly that the complexity is limited, in particular we conjecture that there are no new leading singularities at beyond 3p loops for NpMHV amplitudes.
Leading singularities are invariants of multi-loop scattering amplitudes (the full amplitude at tree level) obtained by generalized unitarity. In this talk we show how to construct multi-loop leading singularities on twistor space for maximally super-symmetric Yang-Mills (and gravity). Building on the tree-level twistor-string representation of scattering amplitudes, they can be represented as integrals over a moduli space of nodal curves in twistor space. We discuss how this might arise from a conjectural twistor-string path integral representation for the full loop amplitude. We also show how the construction relates to the Grassmannian representation of leading singularities conjectured by Arkani-Hamed et. al.. This shows firstly that all leading singularities can be represented in the Grassmannian, and secondly that the complexity is limited, in particular we conjecture that there are no new leading singularities at beyond 3p loops for NpMHV amplitudes.
Posted by: QMW
Wed
27 Jan 2010
Hidden Structures of the S-Matrix
📍 London
Andi Brandhuber
(Queen Mary)
Tue
26 Jan 2010
Matrix Product States and Conformal Field Theory
German Sierra Rodero
(Instituto de Fisica Teorica CSIC-UAM, Madrid)
Abstract:
One dimensional spin chains systems represent an ideal place to study a wide range of non perturbative phenomena such as exotic phases, fractional excitations and statistics. A method to study these systems is the so called Matrix Product States, which provides an ansatz for the ground state and excitations. The MPS method exploits the entanglement properties of spin chains but it is limited to describe systems with short range entanglement. For this reason it cannot properly describe critical
systems where the entanglement entropy grows with the size. In this talk we shall present an extension of the MPS which overcomes this difficulty using Conformal Field Theory. The ansatzs so obtained have strong resemblences with the Laughlin wave function of the Fractional Hall effect.
One dimensional spin chains systems represent an ideal place to study a wide range of non perturbative phenomena such as exotic phases, fractional excitations and statistics. A method to study these systems is the so called Matrix Product States, which provides an ansatz for the ground state and excitations. The MPS method exploits the entanglement properties of spin chains but it is limited to describe systems with short range entanglement. For this reason it cannot properly describe critical
systems where the entanglement entropy grows with the size. In this talk we shall present an extension of the MPS which overcomes this difficulty using Conformal Field Theory. The ansatzs so obtained have strong resemblences with the Laughlin wave function of the Fractional Hall effect.
Posted by: KCL
Tue
26 Jan 2010
Y-system for AdS/CFT and quasi-classical strings in AdS5xS5
Nikolay Gromov
(Hamburg)
Abstract:
Recently Kazakov, Vieira and the author conjectured the Y system set
of equations describing the planar spectrum of AdS/CFT. In this paper
we solve the Y system equations in the strong coupling scaling limit.
We show that the quasiclassical spectrum of string moving inside AdS3
x S1 matches precisely with the prediction of the Y system. Thus the
Y system, unlike the asymptotic Bethe ansatz, describes correctly the
spectrum of one-loop string energies including all exponential finite
size corrections. This gives a very non-trivial further support in
favor of the conjecture. We also discuss how the generalization to the
full AdS5 x S5 can be easily constructed using the PSU(2,2 4) symmetry of the problem.
Recently Kazakov, Vieira and the author conjectured the Y system set
of equations describing the planar spectrum of AdS/CFT. In this paper
we solve the Y system equations in the strong coupling scaling limit.
We show that the quasiclassical spectrum of string moving inside AdS3
x S1 matches precisely with the prediction of the Y system. Thus the
Y system, unlike the asymptotic Bethe ansatz, describes correctly the
spectrum of one-loop string energies including all exponential finite
size corrections. This gives a very non-trivial further support in
favor of the conjecture. We also discuss how the generalization to the
full AdS5 x S5 can be easily constructed using the PSU(2,2 4) symmetry of the problem.
Posted by: IC
Mon
25 Jan 2010
New results on 4D N=2 superconformal sigma-models
Sergei Kuzenko
(University of Western Australia)
Abstract:
Based on the results of 0906.4393 and 0910.5771, this talk will discuss
the formulation of general 4D N=2 superconformal sigma-model in N=2 and N=1 superspace settings.
Based on the results of 0906.4393 and 0910.5771, this talk will discuss
the formulation of general 4D N=2 superconformal sigma-model in N=2 and N=1 superspace settings.
Posted by: IC
Wed
20 Jan 2010
A Three - Generation Calabi-Yau Manifold with Small Hodge Numbers
📍 London
Philip Candelas
(Oxford University)
Abstract:
A complete intersection Calabi-Yau manifold Y, will be presented. This manifold that has Euler number -72 and admits free actions by two groups of automorphisms of order 12. These are the cyclic group Z12 and the non-Abelian dicyclic group Dic3. The quotient manifolds have chi=-6 and Hodge numbers (h11, h21) = (1,4). With the standard embedding of the spin connection in the gauge group, Y gives rise to an E6 gauge theory with 3 chiral generations of particles. The gauge group may be broken further by means of the Hosotani mechanism combined with continuous deformation of the background gauge field.
For the non-Abelian quotient we obtain a model with 3 generations with the gauge group broken to that of the standard model. Moreover there is a limit in which the quotients develop 3 conifold points. These singularities may be resolved simultaneously to give another manifold with (h11, h21) = (2,2) that lies right at the tip of the distribution of Calabi-Yau manifolds. This strongly suggests that there is a heterotic vacuum for this manifold that derives from the 3 generation model on the quotient of Y. The manifold Y may also be realised as a hypersurface in the toric variety. The symmetry group does not act torically, nevertheless we are able to identify the mirror of the quotient manifold by adapting the construction of Batyrev.
A complete intersection Calabi-Yau manifold Y, will be presented. This manifold that has Euler number -72 and admits free actions by two groups of automorphisms of order 12. These are the cyclic group Z12 and the non-Abelian dicyclic group Dic3. The quotient manifolds have chi=-6 and Hodge numbers (h11, h21) = (1,4). With the standard embedding of the spin connection in the gauge group, Y gives rise to an E6 gauge theory with 3 chiral generations of particles. The gauge group may be broken further by means of the Hosotani mechanism combined with continuous deformation of the background gauge field.
For the non-Abelian quotient we obtain a model with 3 generations with the gauge group broken to that of the standard model. Moreover there is a limit in which the quotients develop 3 conifold points. These singularities may be resolved simultaneously to give another manifold with (h11, h21) = (2,2) that lies right at the tip of the distribution of Calabi-Yau manifolds. This strongly suggests that there is a heterotic vacuum for this manifold that derives from the 3 generation model on the quotient of Y. The manifold Y may also be realised as a hypersurface in the toric variety. The symmetry group does not act torically, nevertheless we are able to identify the mirror of the quotient manifold by adapting the construction of Batyrev.
Posted by: IC
Wed
20 Jan 2010
The transplanckian S-matrix: recent progress and open problems
📍 London
Gabriele Veneziano
(College de France)
Abstract:
After a quick review of transplanckian-energy string collisions I will focus on a recent S-matrix approach to gravitational scattering and on its surprisingly good consistency with known results in classical gravitational collapse. A number of yet unresolved issues will also be presented.
After a quick review of transplanckian-energy string collisions I will focus on a recent S-matrix approach to gravitational scattering and on its surprisingly good consistency with known results in classical gravitational collapse. A number of yet unresolved issues will also be presented.
Posted by: QMW
Tue
19 Jan 2010
Making sense of non-Hermitian Hamiltonians
Carl Bender
(Washington University, St. Louis)
Abstract:
The average quantum physicist on the street believes that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy
eigenvalues are real and that time evolution is unitary.
However, the Hamiltonian H=p2+ix3, which is obviously not Dirac Hermitian, has a real positive discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory.
Evidently, the axiom of Dirac Hermiticity is too restrictive. While H=p2+ix3 isnot Dirac Hermitian,
it is PT symmetric, that is, invariant under combined space reflection P and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new
kinds of theories having strange and remarkable properties emerge. Some of these properties have recently been verified in laboratory experiments. If one generalizes classical mechanics into the complex domain, the resulting theories
have equally remarkable properties.
The average quantum physicist on the street believes that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy
eigenvalues are real and that time evolution is unitary.
However, the Hamiltonian H=p2+ix3, which is obviously not Dirac Hermitian, has a real positive discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory.
Evidently, the axiom of Dirac Hermiticity is too restrictive. While H=p2+ix3 isnot Dirac Hermitian,
it is PT symmetric, that is, invariant under combined space reflection P and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new
kinds of theories having strange and remarkable properties emerge. Some of these properties have recently been verified in laboratory experiments. If one generalizes classical mechanics into the complex domain, the resulting theories
have equally remarkable properties.
Posted by: KCL
Sun
17 Jan 2010
Gradient formula for the beta function of 2d quantum field theory
Anatoly Konechny
(Heriot-Watt)
Abstract:
I will explain a gradient formula for beta functions of two-dimensional
quantum field theories. The gradient formula has the form derivative c = - (gij+Delta gij+bij) bj where bj are the beta functions, c and gij are the Zamolodchikov c-function and metric, bij is an antisymmetric tensor introduced by H. Osborn and Delta gij is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.
I will explain a gradient formula for beta functions of two-dimensional
quantum field theories. The gradient formula has the form derivative c = - (gij+Delta gij+bij) bj where bj are the beta functions, c and gij are the Zamolodchikov c-function and metric, bij is an antisymmetric tensor introduced by H. Osborn and Delta gij is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.
Posted by: IC
Thu
14 Jan 2010
(Super)conformal Symmetry of Scattering Amplitudes in N=4 SYM
Niklas Beisert
(MPI, Potsdam)
Abstract:
Tremendous progress in computing perturbative scattering amplitudes
in N=4 supersymmetric gauge theory has been made over the past few
years. Importantly the planar amplitudes appear to display a dual
conformal invariance next to the usual conformal symmetry. Altogether
the symmetry enlarges to a Yangian algebra known from the context of
integrable models. This infinite-dimensional symmetry might have the
power to completely fix the S-matrix by algebraic means.
In this talk we review the above developments. We then discuss
conformal symmetry for tree and loop scattering amplitudes. It turns
out that the free conformal symmetry generators are anomalous which
calls for certain deformations to make the symmetries exact. These
relate amplitude with different numbers of legs, and thus they
contribute substantially to a complete algebraic determination.
Tremendous progress in computing perturbative scattering amplitudes
in N=4 supersymmetric gauge theory has been made over the past few
years. Importantly the planar amplitudes appear to display a dual
conformal invariance next to the usual conformal symmetry. Altogether
the symmetry enlarges to a Yangian algebra known from the context of
integrable models. This infinite-dimensional symmetry might have the
power to completely fix the S-matrix by algebraic means.
In this talk we review the above developments. We then discuss
conformal symmetry for tree and loop scattering amplitudes. It turns
out that the free conformal symmetry generators are anomalous which
calls for certain deformations to make the symmetries exact. These
relate amplitude with different numbers of legs, and thus they
contribute substantially to a complete algebraic determination.
Posted by: QMW
Wed
13 Jan 2010
M2-branes at hypersurface singularities and their deformations
📍 London
James Sparks
(Oxford)
Wed
13 Jan 2010
A-field and B-field from Freed-Witten anomaly
Rafaelle Savelli
(SISSA)
Abstract:
Freed-Witten anomaly is a global ambiguity of the string path integral
measure in the presence of D-branes. It turns out it uniquely
determines,
by imposing its cancellation, the topological type of both the A and
the B
fields when restricted to the brane, as it naturally involves the
interplay between open and closed string degrees of freedom. After
introducing the suitable mathematical framework provided by the
theory of
gerbes with connections, I will try to characterize the nature of the
gauge bundle on a brane in the most general closed string background.
Furthermore, I will go over a case by case analysis, focusing on how it
can account for fractional RR and Page charges and showing the physical
relevance of the resulting K-theoretical improvement for classifying
D-brane charges.
Reference: L. Bonora, F. Ferrari Ruffino, R. S., arXiv: 0810.4291
Freed-Witten anomaly is a global ambiguity of the string path integral
measure in the presence of D-branes. It turns out it uniquely
determines,
by imposing its cancellation, the topological type of both the A and
the B
fields when restricted to the brane, as it naturally involves the
interplay between open and closed string degrees of freedom. After
introducing the suitable mathematical framework provided by the
theory of
gerbes with connections, I will try to characterize the nature of the
gauge bundle on a brane in the most general closed string background.
Furthermore, I will go over a case by case analysis, focusing on how it
can account for fractional RR and Page charges and showing the physical
relevance of the resulting K-theoretical improvement for classifying
D-brane charges.
Reference: L. Bonora, F. Ferrari Ruffino, R. S., arXiv: 0810.4291
Posted by: IC