Triangle Seminars
December 2010
Wed
15 Dec 2010
Geometry of Supermagnets
Volker Schomerus
(DESY)
Wed
15 Dec 2010
Toward All-loop Scattering Amplitudes in N=4 SY
Tristan A. McLoughlin
(MPI)
Tue
14 Dec 2010
Travelling Front of the Decaying Brane
Debashis Ghoshal
(Jawaharlal Nehru University, India)
Abstract:
Some of the perturbative vacua of open string theory are
known to be unstable. They decay to other (meta-)stable vacua. We will consider the dynamics of this relaxation process (decay). In particular, the equation that describes an inhomogeneous decay turns out to be a variant of a non-linear partial differential equation that appears in many other areas. We will point out their similarities and differences.
Some of the perturbative vacua of open string theory are
known to be unstable. They decay to other (meta-)stable vacua. We will consider the dynamics of this relaxation process (decay). In particular, the equation that describes an inhomogeneous decay turns out to be a variant of a non-linear partial differential equation that appears in many other areas. We will point out their similarities and differences.
Posted by: QMW
Mon
13 Dec 2010
3d N=2 gauge theories for M2-branes at toric CY4 cones and the uplift of D6-branes
📍 London
Stefano Cremonesi
(Tel Aviv University)
Abstract:
I will review recent progress in understanding the 3d N=2
superconformal field theories which describe the low energy dynamics
of M2-branes probing toric CY_4 cones in M-theory, based on a KK
reduction of M-theory to type IIA string theory.
A key role in field theory is played by 't Hooft monopole operators,
disorder operators which encode the geometric details of the reduction.
I will review recent progress in understanding the 3d N=2
superconformal field theories which describe the low energy dynamics
of M2-branes probing toric CY_4 cones in M-theory, based on a KK
reduction of M-theory to type IIA string theory.
A key role in field theory is played by 't Hooft monopole operators,
disorder operators which encode the geometric details of the reduction.
Posted by: KCL
Thu
9 Dec 2010
Invariants, symmetries and divergences
Paul Howe
(KC)
Abstract:
Supersymmetric invariants, their symmetries and various approaches to contructing them are discussed. Their role in investigating the onset of UV divergences is outlined. In particular, it is argued that D=4 N=8 supergravity is finite up to, and including, 6 loops.
Supersymmetric invariants, their symmetries and various approaches to contructing them are discussed. Their role in investigating the onset of UV divergences is outlined. In particular, it is argued that D=4 N=8 supergravity is finite up to, and including, 6 loops.
Posted by: QMW
Wed
8 Dec 2010
Non-Kahler geometries in String Theory
📍 London
Dario Martelli
(King's)
Abstract:
After briefly reviewing the notion of geometries characterised by SU(3) structures, I will discuss a particular class
known (in String Theory) as non-Kahler. I will explain how this arises both in Type II and Heterotic Supergravities.
Two explicit constructions of these geometries will be discussed. One is a one-parameter solution corresponding
to fivebranes wrapped on the two-sphere of the resolved conifold, that can be thought of as a non-Kahler analog of the conifold.
The other is a general construction of one-parameter non-Kahler deformations of Calabi-Yau manifolds with a U(1)
isometry, where the non-Abelian Yang-Mills field of the Heterotic is non-trivial. The presentation will be loosely based
on the two papers: arXiv:0906.0591 and arXiv:1010.4031.
After briefly reviewing the notion of geometries characterised by SU(3) structures, I will discuss a particular class
known (in String Theory) as non-Kahler. I will explain how this arises both in Type II and Heterotic Supergravities.
Two explicit constructions of these geometries will be discussed. One is a one-parameter solution corresponding
to fivebranes wrapped on the two-sphere of the resolved conifold, that can be thought of as a non-Kahler analog of the conifold.
The other is a general construction of one-parameter non-Kahler deformations of Calabi-Yau manifolds with a U(1)
isometry, where the non-Abelian Yang-Mills field of the Heterotic is non-trivial. The presentation will be loosely based
on the two papers: arXiv:0906.0591 and arXiv:1010.4031.
Posted by: KCL
Wed
8 Dec 2010
String Vacua with Massive boson-fermion Degeneracy and Non-Singular Cosmology
Ioannis Floriakis
(ENS Paris)
Abstract:
Understanding the phases of string theory in the strong curvature
and high temperature regime, which is inaccessible to the field theory approximation, may provide insights about the physics of the very early Universe. Cosmological solutions can be described at the perturbative string level, arising as quantum or thermal instabilities of an initially flat background. Two major obstacles that typically prevent a perturbative treatment of the backreaction are the Hagedorn/tachyonic divergences that occur in such strong curvature and/or high temperature regions and the initial gravitational singularity (Big Bang), that always appears in the field theory approach. In this talk, I will present recent progress in tackling these problems within the framework of perturbative string theory. In particular, I will consider a special toy model whose high degree of symmetry may help uncover the stringy mechanism that protects the cosmological evolution from Hagedorn or gravitational type singularities.
Understanding the phases of string theory in the strong curvature
and high temperature regime, which is inaccessible to the field theory approximation, may provide insights about the physics of the very early Universe. Cosmological solutions can be described at the perturbative string level, arising as quantum or thermal instabilities of an initially flat background. Two major obstacles that typically prevent a perturbative treatment of the backreaction are the Hagedorn/tachyonic divergences that occur in such strong curvature and/or high temperature regions and the initial gravitational singularity (Big Bang), that always appears in the field theory approach. In this talk, I will present recent progress in tackling these problems within the framework of perturbative string theory. In particular, I will consider a special toy model whose high degree of symmetry may help uncover the stringy mechanism that protects the cosmological evolution from Hagedorn or gravitational type singularities.
Posted by: IC
Tue
7 Dec 2010
Commuting conjugacy classes in groups
Mark Wildon
(Royal Holloway)
Abstract:
Let us say that two conjugacy classes of a group commute if they contain representatives that commute. When G is a finite group with a normal subgroup N such that G/N is cyclic, one can use this definition, together with Hall's Marriage Theorem, to describe the distribution of the conjugacy classes of G across the cosets of N. I will give an overview of this result, and then talk about some more recent work on commuting conjugacy classes in symmetric and general linear groups. This talk is on joint work with John Britnell.
Let us say that two conjugacy classes of a group commute if they contain representatives that commute. When G is a finite group with a normal subgroup N such that G/N is cyclic, one can use this definition, together with Hall's Marriage Theorem, to describe the distribution of the conjugacy classes of G across the cosets of N. I will give an overview of this result, and then talk about some more recent work on commuting conjugacy classes in symmetric and general linear groups. This talk is on joint work with John Britnell.
Posted by: KCL
Thu
2 Dec 2010
Semiclassical strings exactly
Valentina Forini
(AEI)
Abstract:
I will derive exact analytical expressions for the one-loop partition functions of two nontrivial string configurations in AdS5xS5: a folded, spinning string and a string with world-surface ending on two anti-parallel lines. This way, and via AdS/CFT, one can obtain interesting information on the strong coupling structure of anomalous dimensions for the gauge operators dual to the spinning string, as well as compute the first strong coupling correction to the quark-antiquark potential as defined in N =4 SYM.
I will derive exact analytical expressions for the one-loop partition functions of two nontrivial string configurations in AdS5xS5: a folded, spinning string and a string with world-surface ending on two anti-parallel lines. This way, and via AdS/CFT, one can obtain interesting information on the strong coupling structure of anomalous dimensions for the gauge operators dual to the spinning string, as well as compute the first strong coupling correction to the quark-antiquark potential as defined in N =4 SYM.
Posted by: QMW
Wed
1 Dec 2010
Simplicity of scattering amplitudes and Wilson loops
📍 London
Gabriele Travaglini
(Queen Mary)
Wed
1 Dec 2010
Schrodinger Holography
Marika Taylor
(University of Amsterdam)
Abstract:
Abstract: There has recently been considerable discussion of holographic backgrounds with Schrodinger and Lifshitz symmetry, motivated by condensed matter applications. Since the bulk spacetimes are not asymptotically AdS, there are however many subtleties in setting up a holographic dictionary. In this talk we will argue that Schrodinger spacetimes (along with some realizations of Lifshitz) can be understood in terms of deformations of conformal field theories which break the relativistic scaling symmetry, but preserve an anisotropic/non-relativistic scale symmetry. We will highlight how this fact restricts which condensed matter systems can be well modeled holographically, and we will briefly discuss how the entropy of Schrodinger black holes (so-callsed null warped black holes) in three dimensions can be understood in this framework.
Abstract: There has recently been considerable discussion of holographic backgrounds with Schrodinger and Lifshitz symmetry, motivated by condensed matter applications. Since the bulk spacetimes are not asymptotically AdS, there are however many subtleties in setting up a holographic dictionary. In this talk we will argue that Schrodinger spacetimes (along with some realizations of Lifshitz) can be understood in terms of deformations of conformal field theories which break the relativistic scaling symmetry, but preserve an anisotropic/non-relativistic scale symmetry. We will highlight how this fact restricts which condensed matter systems can be well modeled holographically, and we will briefly discuss how the entropy of Schrodinger black holes (so-callsed null warped black holes) in three dimensions can be understood in this framework.
Posted by: IC
November 2010
Thu
25 Nov 2010
Cusp anomaly and integrability from string theory
Riccardo Ricci
(Imperial)
Abstract:
According to the AdS/CFT duality a remarkable correspondence exists between strings in AdS and operators in N=4 SYM. A particularly important case is that of folded strings and the so called twist-operators in gauge theory. This is a remarkable tool for uncovering and checking the detailed structure of the AdS/CFT correspondence and its integrability. In this talk I will show how to match the expression of the anomalous dimension of twist operators
(cusp anomaly) as computed in string theory with the result obtained from the Bethe ansatz of SYM. This agreement resolves a long-standing disagreement between gauge and string sides of the AdS/CFT duality and provides a highly nontrivial strong coupling test of SYM integrability. I will also comment on the computation of finite size corrections to the cusp anomaly.
According to the AdS/CFT duality a remarkable correspondence exists between strings in AdS and operators in N=4 SYM. A particularly important case is that of folded strings and the so called twist-operators in gauge theory. This is a remarkable tool for uncovering and checking the detailed structure of the AdS/CFT correspondence and its integrability. In this talk I will show how to match the expression of the anomalous dimension of twist operators
(cusp anomaly) as computed in string theory with the result obtained from the Bethe ansatz of SYM. This agreement resolves a long-standing disagreement between gauge and string sides of the AdS/CFT duality and provides a highly nontrivial strong coupling test of SYM integrability. I will also comment on the computation of finite size corrections to the cusp anomaly.
Posted by: QMW
Wed
24 Nov 2010
Tailoring Three-Point Functions and Integrability
📍 London
Pedro Vieira
(Perimeter Institute)
Wed
24 Nov 2010
Consistent truncations of type IIB supergravity and holography
Davide Cassani
(Padova)
Abstract:
In the context of gauge-gravity duality, consistent truncations have proved to
be powerful solution-generating tools, their latest application being to the
holographic description of condensed matter systems. In the talk, I will
discuss a rich class of consistent truncations of type IIB supergravity on
squashed Sasaki-Einstein manifolds, leading to N=4 or N=2 gauged supergravity in five dimensions. As examples of the several possible applications, I will present an approach to domain wall gradient flows, as well as a new class of AdS5 backgrounds on the T(1,1) coset, with a comment on some related Lifshitz solutions.
In the context of gauge-gravity duality, consistent truncations have proved to
be powerful solution-generating tools, their latest application being to the
holographic description of condensed matter systems. In the talk, I will
discuss a rich class of consistent truncations of type IIB supergravity on
squashed Sasaki-Einstein manifolds, leading to N=4 or N=2 gauged supergravity in five dimensions. As examples of the several possible applications, I will present an approach to domain wall gradient flows, as well as a new class of AdS5 backgrounds on the T(1,1) coset, with a comment on some related Lifshitz solutions.
Posted by: IC
Tue
23 Nov 2010
Scaling and integrability from AdS5 x S5
Riccardo Ricci
(Imperial College)
Abstract:
According to AdS/CFT a remarkable correspondence exists between strings in AdS5 x S5 and operators in N=4 SYM. A particularly important case is that of fast-spinning folded closed strings and the so called twist-operators in the gauge theory. This is a remarkable tool for uncovering and checking the detailed structure of the AdS/CFT correspondence and its integrability properties.
In this talk I will show how to match the expression of the anomalous dimension of twist operators as computed from the quantum superstring with the result obtained from the Bethe ansatz of SYM. This agreement resolves a long-standing disagreement between gauge and string sides of the AdS/CFT duality and provides a highly nontrivial strong coupling test of SYM integrability.
According to AdS/CFT a remarkable correspondence exists between strings in AdS5 x S5 and operators in N=4 SYM. A particularly important case is that of fast-spinning folded closed strings and the so called twist-operators in the gauge theory. This is a remarkable tool for uncovering and checking the detailed structure of the AdS/CFT correspondence and its integrability properties.
In this talk I will show how to match the expression of the anomalous dimension of twist operators as computed from the quantum superstring with the result obtained from the Bethe ansatz of SYM. This agreement resolves a long-standing disagreement between gauge and string sides of the AdS/CFT duality and provides a highly nontrivial strong coupling test of SYM integrability.
Posted by: KCL
Wed
17 Nov 2010
Hilbert Series: Two Applications
Amihay Hanany
(Imperial College)
Abstract:
This talk will cover two different applications in the study of Hilbert Series. One is in the text book problem of the massive spectrum of the perturbative string in 10 dimensions. We will write the well known partition function in a new form which is covariant under the little group for massive representations. A second application is in the study of flavor invariants in the standard model. We will compute and count all possible invariants which can be constructed from various mass matrices. These two applications are examples of a larger program in which one can use Hilbert series for a collection of problems in physics.
..
(Room EB1 is on the lower ground floor of the Queens' building, which is just in front of the Physics building. It's signed as number 16 on the map
http://www.qmul.ac.uk/docs/about/26065.pdf
The most convenient entrance is on the east side (again just in front of the Physics building): you go down the stairs to the LG floor and then the room is on your right.)
This talk will cover two different applications in the study of Hilbert Series. One is in the text book problem of the massive spectrum of the perturbative string in 10 dimensions. We will write the well known partition function in a new form which is covariant under the little group for massive representations. A second application is in the study of flavor invariants in the standard model. We will compute and count all possible invariants which can be constructed from various mass matrices. These two applications are examples of a larger program in which one can use Hilbert series for a collection of problems in physics.
..
(Room EB1 is on the lower ground floor of the Queens' building, which is just in front of the Physics building. It's signed as number 16 on the map
http://www.qmul.ac.uk/docs/about/26065.pdf
The most convenient entrance is on the east side (again just in front of the Physics building): you go down the stairs to the LG floor and then the room is on your right.)
Posted by: IC
Wed
17 Nov 2010
Searching for supersymmetry and strings and the LHC
John Ellis
(CERN/KCL)
Tue
16 Nov 2010
Brauer trees for finite reductive groups
Olivier Dudas
(Oxford University)
Abstract:
Some aspects of the modular representation theory of a finite group can be
described by a tree. Such trees have been determined for almost all finite
simple groups, but some cases remain unknown. Starting from the example of
the group SL2(q) I will explain how geometric methods can be used to solve
this problem for finite reductive groups.
Some aspects of the modular representation theory of a finite group can be
described by a tree. Such trees have been determined for almost all finite
simple groups, but some cases remain unknown. Starting from the example of
the group SL2(q) I will explain how geometric methods can be used to solve
this problem for finite reductive groups.
Posted by: KCL
Fri
12 Nov 2010
Enthalpy, Areas and Inequalities for Black Holes in Gauged Supergravities
Chris Pope
(Texas / Cambridge)
Abstract:
Various aspects of the geometry and the thermodynamics of black holes in gauged supergravities are explored. In such theories, where the gauge coupling or the cosmological constant can be thought of as an integration constant arising from a higher-dimensional origin, it becomes appropriate to think of it as an additional thermodynamic variable associated with a pressure. The conjugate variable defines a volume for the black hole,
although its geometric interpretation becomes quite subtle if the black
hole is rotating. Further geometric properties of the black holes are
also explored, including an intriguing universal structure for the product
of the horizon areas, which is suggestive of a possible dual field theory
explanation for the microscopic entropy. Isoperimetric and hoop
inequalities are also discussed.
Various aspects of the geometry and the thermodynamics of black holes in gauged supergravities are explored. In such theories, where the gauge coupling or the cosmological constant can be thought of as an integration constant arising from a higher-dimensional origin, it becomes appropriate to think of it as an additional thermodynamic variable associated with a pressure. The conjugate variable defines a volume for the black hole,
although its geometric interpretation becomes quite subtle if the black
hole is rotating. Further geometric properties of the black holes are
also explored, including an intriguing universal structure for the product
of the horizon areas, which is suggestive of a possible dual field theory
explanation for the microscopic entropy. Isoperimetric and hoop
inequalities are also discussed.
Posted by: IC
Thu
11 Nov 2010
Dualities for scattering amplitudes in maximally supersymmetric Yang-Mills theory
Gregory Korchemsky
(Saclay)
Abstract:
I will review a recent progress in computing scattering amplitudes in N=4 SYM theory and explain the recently found duality between MHV gluon scattering amplitudes and correlation functions of half-BPS protected operators in the limit where
the positions of the adjacent operators become light-like separated.
I will review a recent progress in computing scattering amplitudes in N=4 SYM theory and explain the recently found duality between MHV gluon scattering amplitudes and correlation functions of half-BPS protected operators in the limit where
the positions of the adjacent operators become light-like separated.
Posted by: QMW
Wed
10 Nov 2010
Y-system for AdS/CFT
📍 London
Nikolay Gromov
(King's)
Abstract:
The Y-system, originating from integrability, is a tool
describing the exact spectrum in 4D N=4 Super-Yang-Mills theory in
a planar limit. We describe the construction and discuss predictions
and tests for weak, strong and intermediate couplings.
The Y-system, originating from integrability, is a tool
describing the exact spectrum in 4D N=4 Super-Yang-Mills theory in
a planar limit. We describe the construction and discuss predictions
and tests for weak, strong and intermediate couplings.
Posted by: KCL
Wed
10 Nov 2010
Supersymmetric 3-algebra theories in 6 dimensions
Costis Papageorgakis
(KCL)
Abstract:
Using 3-algebras we obtain a nonabelian system of equations that furnish a representation of the (2,0)-supersymmetric tensor multiplet. The on-shell conditions are quite restrictive so that the system can be reduced to five-dimensional super-Yang-Mills theory along with six-dimensional abelian (2,0) tensor multiplets. Possible applications to D4-branes and M5-branes are discussed.
Using 3-algebras we obtain a nonabelian system of equations that furnish a representation of the (2,0)-supersymmetric tensor multiplet. The on-shell conditions are quite restrictive so that the system can be reduced to five-dimensional super-Yang-Mills theory along with six-dimensional abelian (2,0) tensor multiplets. Possible applications to D4-branes and M5-branes are discussed.
Posted by: IC
Tue
9 Nov 2010
Evolution as an information dynamic system
Roman Belavkin
(Middlesex University)
Abstract:
I will speak about a new research project called 'Evolution as an information dynamic system', which involves collaboration between four universities in the United Kingdom. This is a three year project started this year, 2010, and its aim is to develop new understanding of information dynamics in evolution and biology. In particular, we are going to derive new optimality conditions for some evolutionary operators, such as mutation and recombination. Evolutionary states will be represented by probability measures on the space of genetic sequences, and different operators produce different evolution of the states. We define the optimality conditions for evolution based on the maximisation of utility (or fitness) of information principle. The optimal evolution in this sense achieves the shortest 'information distance', and it can be different from an evolution optimal in another sense, such as the shortest convergence time. We argue that the former achieves a better adaptation of organisms living in a dynam
ic environment. I will present several early results related to the optimisation of mutation rate parameter. I will review these results in the light of the classical theories of adaptation (e.g. Fisher's geometric model) and error threshold. Then I will outline some future theoretical and experimental work of the project.
I will speak about a new research project called 'Evolution as an information dynamic system', which involves collaboration between four universities in the United Kingdom. This is a three year project started this year, 2010, and its aim is to develop new understanding of information dynamics in evolution and biology. In particular, we are going to derive new optimality conditions for some evolutionary operators, such as mutation and recombination. Evolutionary states will be represented by probability measures on the space of genetic sequences, and different operators produce different evolution of the states. We define the optimality conditions for evolution based on the maximisation of utility (or fitness) of information principle. The optimal evolution in this sense achieves the shortest 'information distance', and it can be different from an evolution optimal in another sense, such as the shortest convergence time. We argue that the former achieves a better adaptation of organisms living in a dynam
ic environment. I will present several early results related to the optimisation of mutation rate parameter. I will review these results in the light of the classical theories of adaptation (e.g. Fisher's geometric model) and error threshold. Then I will outline some future theoretical and experimental work of the project.
Posted by: KCL
Fri
5 Nov 2010
Quantum Riemann Surfaces
📍 London
Tudor Dimofte
(DAMTP)
Abstract:
Quantized complex curves play a central role in both topological string
theory and Chern-Simons theory with complexified gauge group. In both cases these
quantum curves yield operators that annihilate partition functions. However, in
both cases, the actual quantization of these curves has only been understood
indirectly (via matrix models on one hand, via recursion relations for the Jones
polynomial on the other). I will discuss an intrinsic, geometric quantization scheme
that should produce such quantum Riemann surfaces directly.
N.B. Such quantum curves also show up in conformal field theory, as the operators
that annihilate correlators with degenerate insertions.
Quantized complex curves play a central role in both topological string
theory and Chern-Simons theory with complexified gauge group. In both cases these
quantum curves yield operators that annihilate partition functions. However, in
both cases, the actual quantization of these curves has only been understood
indirectly (via matrix models on one hand, via recursion relations for the Jones
polynomial on the other). I will discuss an intrinsic, geometric quantization scheme
that should produce such quantum Riemann surfaces directly.
N.B. Such quantum curves also show up in conformal field theory, as the operators
that annihilate correlators with degenerate insertions.
Posted by: KCL
Thu
4 Nov 2010
The triangulation of moduli spaces of pointed Riemann surfaces by ribbon graphs
Eduard Looijenga
(Utrecht)
Abstract:
Mumford and Thurston observed that the theory of Jenkins-Strebel differentials can be used to triangulate a compactification of the moduli space of n-pointed Riemann surfaces of given genus. This was later exploited by Kontsevich to prove the Witten conjecture. We review this construction, make a comparison with the Deligne-Mumford compacfication and discuss some of the conjectures in algebraic geometry it led to.
Mumford and Thurston observed that the theory of Jenkins-Strebel differentials can be used to triangulate a compactification of the moduli space of n-pointed Riemann surfaces of given genus. This was later exploited by Kontsevich to prove the Witten conjecture. We review this construction, make a comparison with the Deligne-Mumford compacfication and discuss some of the conjectures in algebraic geometry it led to.
Posted by: QMW
Wed
3 Nov 2010
Aspects of defects in integrable models
📍 London
Edward Corrigan
(Durham)
Abstract:
Though defects in a general sense are ubiquitous and much-studied
within statistical mechanics models it is only recently that they have been
considered within integrable field theory. At first sight, defects could be
considered disastrous since the property of integrability might be lost.
However, it turns out that not only is it possible to have 'integrable
defects' but they have a range of interesting properties and cast some new
light on traditional features. Several examples will be described, together
with their properties in classical and quantum versions of the models.
Though defects in a general sense are ubiquitous and much-studied
within statistical mechanics models it is only recently that they have been
considered within integrable field theory. At first sight, defects could be
considered disastrous since the property of integrability might be lost.
However, it turns out that not only is it possible to have 'integrable
defects' but they have a range of interesting properties and cast some new
light on traditional features. Several examples will be described, together
with their properties in classical and quantum versions of the models.
Posted by: KCL
Wed
3 Nov 2010
Interaction Vertices and BCFW Recursion Relations for Higher Spin Fields
Mirian Tsulaia
(Liverpool)
Abstract:
We review a method of the construction of cubic off-shell interaction vertices for Higher Spin fields. This method is based on the BRST approach and is valid both for flat and AdS backgrounds. As a particular illustration of this method we construct an off-shell extension of the vertices which are related to perturbative bosonic string theory. We discus a generalization of this method for higher order vertices and examine whether BCFW recursion relations are applicable for interacting Higher Spin gage theories.
We review a method of the construction of cubic off-shell interaction vertices for Higher Spin fields. This method is based on the BRST approach and is valid both for flat and AdS backgrounds. As a particular illustration of this method we construct an off-shell extension of the vertices which are related to perturbative bosonic string theory. We discus a generalization of this method for higher order vertices and examine whether BCFW recursion relations are applicable for interacting Higher Spin gage theories.
Posted by: IC
Tue
2 Nov 2010
Exact and approximate epidemic models on networks
Istvan Zoltan Kiss
(University of Sussex)
Abstract:
Many if not all models of disease transmission on networks can be
linked to the exact state-based Markovian formulation. However the large
number of equations for any system of realistic size limits their
applicability to small populations. As a result, most modelling work relies
on simulation and pairwise models. In this talk, for a simple
SIS dynamics on an arbitrary network, we formalise the link between a well
known pairwise model and the exact Markovian formulation and we formalise
lumping and its direct link to graph automorphism. Lumping is a powerful
technique that exploits graph symmetry and allows to keep the model exact
while considerably reducing the number of equations. Finally, for pairwise
model two different closures are presented, one well established and one
that has been recently proposed. The closed dynamical systems are solved
numerically and the results are compared to output from individual-based
stochastic simulations. This is done for a range of networks
with the same average degree and clustering coefficient but generated using
different algorithms. It is shown that the ability of the pairwise system
to accurately model an epidemic is fundamentally dependent on the underlying
large-scale network structure. We show that the existing pairwise models
work well for certain types of network but have to be used with caution as
higher-order network structures may compromise their effectiveness.
Keywords: network, epidemic, Markov chain, moment closure.
Many if not all models of disease transmission on networks can be
linked to the exact state-based Markovian formulation. However the large
number of equations for any system of realistic size limits their
applicability to small populations. As a result, most modelling work relies
on simulation and pairwise models. In this talk, for a simple
SIS dynamics on an arbitrary network, we formalise the link between a well
known pairwise model and the exact Markovian formulation and we formalise
lumping and its direct link to graph automorphism. Lumping is a powerful
technique that exploits graph symmetry and allows to keep the model exact
while considerably reducing the number of equations. Finally, for pairwise
model two different closures are presented, one well established and one
that has been recently proposed. The closed dynamical systems are solved
numerically and the results are compared to output from individual-based
stochastic simulations. This is done for a range of networks
with the same average degree and clustering coefficient but generated using
different algorithms. It is shown that the ability of the pairwise system
to accurately model an epidemic is fundamentally dependent on the underlying
large-scale network structure. We show that the existing pairwise models
work well for certain types of network but have to be used with caution as
higher-order network structures may compromise their effectiveness.
Keywords: network, epidemic, Markov chain, moment closure.
Posted by: KCL
October 2010
Thu
28 Oct 2010
Constraining F-theory GUTs
Sakura Schafer-Nameki
(King's)
Abstract:
String theory phenomenology generically suffers from either too much flexibility (and lack of predictability) or from the a high specialization to case by case studies. I will discuss how F-theory GUT model building manages to get around these pitfall, in particular, I will explain, how to systematically include global string consistency conditions, which are independent of the specific compactification, and which come with the benefit of highly constraining the class of GUT models that can arise from F-theory.
String theory phenomenology generically suffers from either too much flexibility (and lack of predictability) or from the a high specialization to case by case studies. I will discuss how F-theory GUT model building manages to get around these pitfall, in particular, I will explain, how to systematically include global string consistency conditions, which are independent of the specific compactification, and which come with the benefit of highly constraining the class of GUT models that can arise from F-theory.
Posted by: QMW
Wed
27 Oct 2010
Lifshitz Solutions in String and M-Theory
📍 London
Aristomenis Donos
(Imperial)
Abstract:
Condensed matter systems at quantum critical points can be described by strongly coupled field theories exhibiting anisotropic scale invariance. Lifshitz geometries been proposed to be holographic duals to these theories. I will discuss top down constructions of Lifshitz geometries in Type IIB and D=11 dimensional supergravities.
Condensed matter systems at quantum critical points can be described by strongly coupled field theories exhibiting anisotropic scale invariance. Lifshitz geometries been proposed to be holographic duals to these theories. I will discuss top down constructions of Lifshitz geometries in Type IIB and D=11 dimensional supergravities.
Posted by: KCL
Wed
27 Oct 2010
Skyrmions, instantons and holography
Paul Sutcliffe
(Durham)
Abstract:
Recently the Skyrme model has been derived from string theory in
the context of holographic QCD. Inspired by this work, I shall
introduce a BPS Skyrme model derived from Yang-Mills theory.
This explains and extends the construction of Skyrmions from the
holonomy of Yang-Mills instantons, introduced some time ago by
Atiyah and Manton
Recently the Skyrme model has been derived from string theory in
the context of holographic QCD. Inspired by this work, I shall
introduce a BPS Skyrme model derived from Yang-Mills theory.
This explains and extends the construction of Skyrmions from the
holonomy of Yang-Mills instantons, introduced some time ago by
Atiyah and Manton
Posted by: IC
Wed
27 Oct 2010
F-enomenology
📍 London
Sakura Schafer-Nameki
(King's)
Abstract:
I will give an overview of recent developments in F-theory GUT
model building. First I will discuss the basic ideas of F-theory model
building, exemplifying this by the construction of supersymmetric SU(5)
GUTs. Then I will outline how global string theoretic consistency
requirements impact the SUSY phenomenology. The main focus of this talk
will be on the phenomenological implications of these models.
I will give an overview of recent developments in F-theory GUT
model building. First I will discuss the basic ideas of F-theory model
building, exemplifying this by the construction of supersymmetric SU(5)
GUTs. Then I will outline how global string theoretic consistency
requirements impact the SUSY phenomenology. The main focus of this talk
will be on the phenomenological implications of these models.
Posted by: KCL
Tue
26 Oct 2010
Modular realizations of hyperbolic Weyl groups
Hermann Nicolai
(Albert Einstein Institute, Golm)
Fri
22 Oct 2010
Freezing transition and replica symmetry breaking in decaying Burgers turbulence via random matrix dualities
Yan Fyodorov
(Nottingham)
Abstract:
We reveal a phase transition with decreasing viscosity in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities. The low-viscosity phase exhibits non-Gaussian one-point probability density of velocities reflecting a spontaneous one step replica symmetry breaking in the associated statistical mechanics problem. We obtain the low orders cumulants analytically. Our results, which are checked numerically, are based on combining insights in the mechanism of the freezing transition in random logarithmic potentials with an extension of duality relations discovered recently in Random Matrix Theory.
(Based on the joint work with Pierre Le Doussal and Alberto Rosso.)
We reveal a phase transition with decreasing viscosity in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities. The low-viscosity phase exhibits non-Gaussian one-point probability density of velocities reflecting a spontaneous one step replica symmetry breaking in the associated statistical mechanics problem. We obtain the low orders cumulants analytically. Our results, which are checked numerically, are based on combining insights in the mechanism of the freezing transition in random logarithmic potentials with an extension of duality relations discovered recently in Random Matrix Theory.
(Based on the joint work with Pierre Le Doussal and Alberto Rosso.)
Posted by: brunel
Thu
21 Oct 2010
Gauge theory non-local operators from two dimensional conformal field theories
Filippo Passerini
(Berlin)
Abstract:
The partition function of a family of four dimensional N=2 gauge theories has been related by Alday, Gaiotto and Tachikawa (AGT) to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A1 conformal Toda field theory, i.e. Liouville theory. In this seminar I
will discuss how the AGT proposal is modified when the gauge theories include non-local operators. I will focus in particular on Wilson loop operators and a certain type of surface operators in SU(N) N=2 gauge theories. For the case of the surface operator, I will show that the relevant two dimensional field theory is a conformal theory with SL(N) affine algebra. This result generalizes the recent result by Alday and Tachikawa that relates SU(2) gauge theories with surface operators to SL(2) affine algebras.
The partition function of a family of four dimensional N=2 gauge theories has been related by Alday, Gaiotto and Tachikawa (AGT) to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A1 conformal Toda field theory, i.e. Liouville theory. In this seminar I
will discuss how the AGT proposal is modified when the gauge theories include non-local operators. I will focus in particular on Wilson loop operators and a certain type of surface operators in SU(N) N=2 gauge theories. For the case of the surface operator, I will show that the relevant two dimensional field theory is a conformal theory with SL(N) affine algebra. This result generalizes the recent result by Alday and Tachikawa that relates SU(2) gauge theories with surface operators to SL(2) affine algebras.
Posted by: QMW
Wed
20 Oct 2010
A supermatrix model for ABJM theory
📍 London
Nadav Drukker
(Imperial)
Abstract:
I will review the matrix model which calculates the partition function of ABJM theory on S3 as well as the expectation value of Wilson loop operators. I will then explain how this matrix model is solved and present the results for these quantities at all values of the couplings. At strong coupling these calculations reproduce the results of supergravity on Ads4 x CP3 and in particular the N to the 3/2 scaling of the free energy of the theory.
I will review the matrix model which calculates the partition function of ABJM theory on S3 as well as the expectation value of Wilson loop operators. I will then explain how this matrix model is solved and present the results for these quantities at all values of the couplings. At strong coupling these calculations reproduce the results of supergravity on Ads4 x CP3 and in particular the N to the 3/2 scaling of the free energy of the theory.
Posted by: KCL
Tue
19 Oct 2010
Use of equivalence theorems for the study of ambiguity in non-Abelian gauge theories
Andrei Slavnov
(Steklov Institute, Moscow)
Tue
19 Oct 2010
Discrete integrable dynamics and Somos sequences
Andrew Hone
(Kent)
Abstract:
Somos sequences are generated by a rational recurrence, which is specified by a quadratic relation
between adjacent iterates. Michael Somos noticed that, for some special choices of initial values, such recurrences
could unexpectedly produce sequences of integers. Examples of Somos sequences were known somewhat earlier in
number theory, from Morgan Ward's elliptic analogues of Fibonacci and Lucas sequences. In algebraic combinatorics,
Somos recurrences provide a basic example of the Laurent phenomenon, which is a cornerstone of Fomin and Zelevinsky's
theory of cluster algebras. This introductory talk reviews the history of Somos sequences and their connections
with these and other areas of mathematics and theoretical physics, including solvable statistical mechanics (the hard hexagon
model) and discrete integrable systems (QRT maps and the discrete Hirota equation).
Somos sequences are generated by a rational recurrence, which is specified by a quadratic relation
between adjacent iterates. Michael Somos noticed that, for some special choices of initial values, such recurrences
could unexpectedly produce sequences of integers. Examples of Somos sequences were known somewhat earlier in
number theory, from Morgan Ward's elliptic analogues of Fibonacci and Lucas sequences. In algebraic combinatorics,
Somos recurrences provide a basic example of the Laurent phenomenon, which is a cornerstone of Fomin and Zelevinsky's
theory of cluster algebras. This introductory talk reviews the history of Somos sequences and their connections
with these and other areas of mathematics and theoretical physics, including solvable statistical mechanics (the hard hexagon
model) and discrete integrable systems (QRT maps and the discrete Hirota equation).
Posted by: KCL
Thu
14 Oct 2010
D-Brane Wess-Zumino Terms and U-Duality
Eric Bergshoeff
(Groningen)
Abstract:
I will show how to construct gauge-invariant and U-duality covariant expressions for
Wess-Zumino terms corresponding to general Dp-branes in arbitrary D less than 10 dimensions.
A distinguishing feature of these Wess-Zumino terms is that they contain twice as
many scalars as the 10-D compactified dimensions, in line with
doubled geometry. It turns out that For D less than 10 the charges of the
higher-dimensional branes can all be expressed as products of the
0-brane charges, which include the D0-brane and the NS-NS 0-brane
charges. I will show how the general expressions for these charges
determine the non-trivial conjugacy class
to which some of the higher-dimensional D-branes belong.
Some implications and extensions of our work will be discussed.
I will show how to construct gauge-invariant and U-duality covariant expressions for
Wess-Zumino terms corresponding to general Dp-branes in arbitrary D less than 10 dimensions.
A distinguishing feature of these Wess-Zumino terms is that they contain twice as
many scalars as the 10-D compactified dimensions, in line with
doubled geometry. It turns out that For D less than 10 the charges of the
higher-dimensional branes can all be expressed as products of the
0-brane charges, which include the D0-brane and the NS-NS 0-brane
charges. I will show how the general expressions for these charges
determine the non-trivial conjugacy class
to which some of the higher-dimensional D-branes belong.
Some implications and extensions of our work will be discussed.
Posted by: QMW
Wed
13 Oct 2010
Unusual singular behavior of the entanglement entropy in one dimension
Francesco Ravanini
(Bologna)
Abstract:
We study the Renyi entropy of the one-dimensional XYZ spin-1/2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tri-critical points where these phases join. Two of these points are described by a conformal field theory and close to them the entropy scales as the logarithm of its mass gap. The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an essential singularity. At these non-conformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. We propose the entropy as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models.
We study the Renyi entropy of the one-dimensional XYZ spin-1/2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tri-critical points where these phases join. Two of these points are described by a conformal field theory and close to them the entropy scales as the logarithm of its mass gap. The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an essential singularity. At these non-conformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. We propose the entropy as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models.
Posted by: KCL
Wed
13 Oct 2010
W-algebras and surface operators in 4d N=2 gauge theories
📍 London
Niclas Wyllard
(Chalmers)
Abstract:
We discuss relations between two a priori unrelated classes of objects: (i) W-algebras, which are certain symmetry algebras of two-dimensional conformal field theories, and (ii) four-dimensional N=2 gauge theories in the presence of surface operators (certain two-dimensional defects). In particular, we relate the classifications of W-algebras and surface operators.
We discuss relations between two a priori unrelated classes of objects: (i) W-algebras, which are certain symmetry algebras of two-dimensional conformal field theories, and (ii) four-dimensional N=2 gauge theories in the presence of surface operators (certain two-dimensional defects). In particular, we relate the classifications of W-algebras and surface operators.
Posted by: QMW
Wed
13 Oct 2010
Black Holes and Exotic Geometries
📍 London
Jan de Boer
(Amsterdam)
Tue
12 Oct 2010
Blood and metal flowing down helical pipes
Jonathan Mestel
(Imperial College)
Abstract:
Helically symmetry is an exact generalisation of two-dimensionality and
axisymmetry.
The flow down a helical pipe is investigated under the assumption of
helical symmetry. The implications for blood flow in the body are
discussed. It is shown that the observed torsion of arteries may have
fluid dynamical benefits.
The blood is then replaced by a liquid metal, and it is found that the
same flow can give rise to the spontaneous generation of magnetic field,
known as a dynamo. Animations, but no experiments will be shown, in the
absence of a volunteer for this surgical procedure.
Helically symmetry is an exact generalisation of two-dimensionality and
axisymmetry.
The flow down a helical pipe is investigated under the assumption of
helical symmetry. The implications for blood flow in the body are
discussed. It is shown that the observed torsion of arteries may have
fluid dynamical benefits.
The blood is then replaced by a liquid metal, and it is found that the
same flow can give rise to the spontaneous generation of magnetic field,
known as a dynamo. Animations, but no experiments will be shown, in the
absence of a volunteer for this surgical procedure.
Posted by: KCL
Fri
8 Oct 2010
Production of a vector boson in association with multiple jets at NLO in QCD at the LHC
Lance Dixon
(SLAC)
Abstract:
Particle group seminar. See more information here:
http://pprc.qmul.ac.uk/seminars/seminars.html
(No seminar in Queen Mary on Thursday.)
Particle group seminar. See more information here:
http://pprc.qmul.ac.uk/seminars/seminars.html
(No seminar in Queen Mary on Thursday.)
Posted by: QMW
Wed
6 Oct 2010
The vertex operator algebra of conformal loop ensembles
📍 London
Benjamin Doyon
(King's)
Abstract:
Vertex operator algebra (VOA) is the algebraic setup formalising conformal field theory. It develops in a mathematically complete way the idea of constructing quantum field theory using the algebra of symmetry currents and their modules. On the other hand, conformal loop ensembles (CLE) are measures on random loop configurations that are known, in certain cases, to describe the continuous limit of statistical models at critical points. There is a one-parameter family of such measures, supposed to correspond to all central charges between 0 and 1. These two constructions enjoy complete mathematical rigour, and give the opportunity to understand with more precision the relation between the statistical interpretation of QFT, and its algebraic description. I will describe some of my recent works in this direction: I will explain how to construct the Virasoro VOA (the stress-energy tensor and its descendents) in terms of random objects in CLE. No prior knowledge of either VOA or CLE is needed as I will review both subjects.
Vertex operator algebra (VOA) is the algebraic setup formalising conformal field theory. It develops in a mathematically complete way the idea of constructing quantum field theory using the algebra of symmetry currents and their modules. On the other hand, conformal loop ensembles (CLE) are measures on random loop configurations that are known, in certain cases, to describe the continuous limit of statistical models at critical points. There is a one-parameter family of such measures, supposed to correspond to all central charges between 0 and 1. These two constructions enjoy complete mathematical rigour, and give the opportunity to understand with more precision the relation between the statistical interpretation of QFT, and its algebraic description. I will describe some of my recent works in this direction: I will explain how to construct the Virasoro VOA (the stress-energy tensor and its descendents) in terms of random objects in CLE. No prior knowledge of either VOA or CLE is needed as I will review both subjects.
Posted by: KCL
Tue
5 Oct 2010
The Goettsche conjecture
Richard Thomas
(Imperial College)
Abstract:
Given an r-dimensional family of degree d plane curves, it is a classical (Victorian) question how many there are with r nodes.
I will attempt to explain what this means, what form Goettsche and others conjectured for the answer (for curves on arbitrary complex surfaces), and a short proof.
Given an r-dimensional family of degree d plane curves, it is a classical (Victorian) question how many there are with r nodes.
I will attempt to explain what this means, what form Goettsche and others conjectured for the answer (for curves on arbitrary complex surfaces), and a short proof.
Posted by: KCL
September 2010
Tue
28 Sep 2010
Magnon dispersion to four loops in the ABJM and ABJ models
Olof Ohlsson-Sax
(Uppsala)
Abstract:
The ABJM model is a superconformal Chern-Simons theory with N = 6 supersymmetry which is believed to be integrable in the planar limit. However, there is a coupling dependent function that appears in the magnon dispersion relation and the asymptotic Bethe ansatz that is only known to leading order at strong and weak coupling. We compute this function to four loops in perturbation theory by an explicit Feynman diagram calculation for both the ABJM model and the ABJ extension. We then compute the four-loop wrapping correction for a scalar operator in the 20 of SU(4) and find that it agrees with a recent prediction from the ABJM Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ model that might be perturbatively integrable at all loop orders but has a short range Hamiltonian.
The ABJM model is a superconformal Chern-Simons theory with N = 6 supersymmetry which is believed to be integrable in the planar limit. However, there is a coupling dependent function that appears in the magnon dispersion relation and the asymptotic Bethe ansatz that is only known to leading order at strong and weak coupling. We compute this function to four loops in perturbation theory by an explicit Feynman diagram calculation for both the ABJM model and the ABJ extension. We then compute the four-loop wrapping correction for a scalar operator in the 20 of SU(4) and find that it agrees with a recent prediction from the ABJM Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ model that might be perturbatively integrable at all loop orders but has a short range Hamiltonian.
Posted by: KCL
Tue
14 Sep 2010
Universality in Quantum Chaos
Sebastian Muller
(Bristol)
Abstract:
Many systems in nature are chaotic, i.e., their classical time evolution depends sensitively on the initial conditions.
This has important consequences for their quantum behaviour. In particular the energy levels of chaotic systems
display universal statistical properties, and have a tendency to repel each other. I will give an introduction into
recent research to explain this universal behaviour. A crucial ingredient is the discovery of correlations between
classical periodic orbits. For example if a periodic orbit contains crosses itself with a small angle there is also
a partner orbit narrowly avoiding that crossing. In a semiclassical approach one sees that contributions of such correlated
orbits can interfere constructively. I will show how this gives rise to universal spectral statistics.
I will also discuss connections to random matrix theory (which gives predictions for spectral statistics) as well as
the combinatorics of permutations.
Many systems in nature are chaotic, i.e., their classical time evolution depends sensitively on the initial conditions.
This has important consequences for their quantum behaviour. In particular the energy levels of chaotic systems
display universal statistical properties, and have a tendency to repel each other. I will give an introduction into
recent research to explain this universal behaviour. A crucial ingredient is the discovery of correlations between
classical periodic orbits. For example if a periodic orbit contains crosses itself with a small angle there is also
a partner orbit narrowly avoiding that crossing. In a semiclassical approach one sees that contributions of such correlated
orbits can interfere constructively. I will show how this gives rise to universal spectral statistics.
I will also discuss connections to random matrix theory (which gives predictions for spectral statistics) as well as
the combinatorics of permutations.
Posted by: QMW
Mon
6 Sep 2010
Extremal black hole entropy
Ashoke Sen
(Harish Chandra)