Triangle Seminars
July 2008
Wed
9 Jul 2008
Sigma models with defects and Fourier-Mukai transforms
📍 London
Gor Sarkissian
(Univ. Hamburg)
Wed
2 Jul 2008
Random-Matrix Theory within Superstatistics
Adel Abul-Magd
(Sinai University)
Abstract:
In analogy to Beck and Cohen's superstatistics (1), we connect the canonical Gaussian ensembles of the random-matrix theory (RMT) to their superstatistical generalizations through the fluctuation of an intensive parameter, the local density of states (2). On one hand, the superstatistical RMT, seen from the present perspective, may bear interest per se because of the additional nontrivial fluctuations introduced in a simple model. On the other hand, it may constitute a useful statistical paradigm for the analysis of the spectral fluctuations of systems with mixed regular-chaotic dynamics. In contrast to other proposals for applying RMT to mixed dynamics, the superstatistical approach yields ensemble of matrices, which are invariant with respect to base transformation. The formalism has been checked by the analysis of experimental resonance spectra of mixed microwave billiards (3). The spectra for each billiard are represented as time series in which the level order plays the role of time. Each series is shown to have two relaxation times as required by superstatistics, which involves the folding of two distribution functions. Analysis of the time series suggests that the superstatistical parameter has an inverse-chi-square distribution. The experimental distribution nearest-neighbor level spacings and strength functions agree with the corresponding predicted distributions.
(1) C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003).
(2) A.Y. Abul-Magd, Phys.Rev. E 71, 066207 (2005).
(3) A.Y. Abul-Magd, B. Dietz, T. Friedrich, and A. Richter, Phys. R
In analogy to Beck and Cohen's superstatistics (1), we connect the canonical Gaussian ensembles of the random-matrix theory (RMT) to their superstatistical generalizations through the fluctuation of an intensive parameter, the local density of states (2). On one hand, the superstatistical RMT, seen from the present perspective, may bear interest per se because of the additional nontrivial fluctuations introduced in a simple model. On the other hand, it may constitute a useful statistical paradigm for the analysis of the spectral fluctuations of systems with mixed regular-chaotic dynamics. In contrast to other proposals for applying RMT to mixed dynamics, the superstatistical approach yields ensemble of matrices, which are invariant with respect to base transformation. The formalism has been checked by the analysis of experimental resonance spectra of mixed microwave billiards (3). The spectra for each billiard are represented as time series in which the level order plays the role of time. Each series is shown to have two relaxation times as required by superstatistics, which involves the folding of two distribution functions. Analysis of the time series suggests that the superstatistical parameter has an inverse-chi-square distribution. The experimental distribution nearest-neighbor level spacings and strength functions agree with the corresponding predicted distributions.
(1) C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003).
(2) A.Y. Abul-Magd, Phys.Rev. E 71, 066207 (2005).
(3) A.Y. Abul-Magd, B. Dietz, T. Friedrich, and A. Richter, Phys. R
Posted by: brunel
June 2008
Fri
13 Jun 2008
Exact diagonalisation of 1D interacting Fermions
Heiner Kohler
(Duisburg-Essen)
Thu
5 Jun 2008
Spiky strings, light-like Wilson loops and the pp-wave anomaly
Martin Kruczenski
(Perdue University)
Abstract:
I am going to review, in the context of gauge theories, the anomalous dimension of twist two operators, the cusp anomaly of Wilson loops and how they relate through AdS/CFT to rotating strings in AdS space. Then I'm going to describe in more detail the spiky strings and their properties for large spin which allows us to obtain a relation between the anomalous dimension of twist two operators and the pp-wave anomaly, an anomaly we find when N=4 SYM theory is put in a pp-wave background. Finally I'm going to consider various new open string solutions describing Wilson loops in a pp-wave and in flat space. Based on 0802.2039 and 0804.3438.
I am going to review, in the context of gauge theories, the anomalous dimension of twist two operators, the cusp anomaly of Wilson loops and how they relate through AdS/CFT to rotating strings in AdS space. Then I'm going to describe in more detail the spiky strings and their properties for large spin which allows us to obtain a relation between the anomalous dimension of twist two operators and the pp-wave anomaly, an anomaly we find when N=4 SYM theory is put in a pp-wave background. Finally I'm going to consider various new open string solutions describing Wilson loops in a pp-wave and in flat space. Based on 0802.2039 and 0804.3438.
Posted by: IC
May 2008
Thu
15 May 2008
Tachyon Condensation on a Separated Brane-Antibrane System
Arjun Bagchi
(Allahabad)
April 2008
Wed
30 Apr 2008
The Hamiltonian structure of the second Painleve hierarchy
Marta Mazzocco
(Manchester)
Abstract:
After a short introduction to the Painleve equations, I'll study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear
ODE of order 2n in the independent variable z depending on n
parameters denoted by t(1),...,t(n-1) and alpha(n). I'll
introduce new canonical coordinates and obtain Hamiltonians for the z and t(1),...,t(n-1) evolutions. I'll give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates.
After a short introduction to the Painleve equations, I'll study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear
ODE of order 2n in the independent variable z depending on n
parameters denoted by t(1),...,t(n-1) and alpha(n). I'll
introduce new canonical coordinates and obtain Hamiltonians for the z and t(1),...,t(n-1) evolutions. I'll give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates.
Posted by: brunel
Wed
30 Apr 2008
Dynamical Generation of Higher Gauge Groups in Matrix Model.
Subrata Bal
(Dublin)
Abstract:
The dynamics of k coincident D-branes in string theory is described
effectively by U(k) Yang-Mills theory at low energy. While these
configurations appear as classical solutions in matrix models, it was
not clear whether it is possible to realize the k =/= 1 case as the
true vacuum. We consider massive Yang-Mills-Chern-Simons matrix model
and investigate the generation of higher gauge groups U(2), U(3) in
this model.
The dynamics of k coincident D-branes in string theory is described
effectively by U(k) Yang-Mills theory at low energy. While these
configurations appear as classical solutions in matrix models, it was
not clear whether it is possible to realize the k =/= 1 case as the
true vacuum. We consider massive Yang-Mills-Chern-Simons matrix model
and investigate the generation of higher gauge groups U(2), U(3) in
this model.
Posted by: QMW
Tue
29 Apr 2008
Extreme Value Statistics, Integer Partitions and Bose Gas
Satya Majumdar
(Paris XI)
Abstract:
In this talk I will first briefly review the extreme value statistics of independent random variables and show how three limiting distributions (Gumbel, Frechet and Weibull distributions) emerge there. Next I'll discuss the celebrated Integer Partition problem of Hardy and Ramanujan and its connection to the ideal Bose gas. We will see how the same three limiting distributions of extreme value statistics appear in the Integer Partion/Bose gas problem. The connection between these three different problems respectively in probability theory, number theory and statistical physics is intriguing and fascinating.
In this talk I will first briefly review the extreme value statistics of independent random variables and show how three limiting distributions (Gumbel, Frechet and Weibull distributions) emerge there. Next I'll discuss the celebrated Integer Partition problem of Hardy and Ramanujan and its connection to the ideal Bose gas. We will see how the same three limiting distributions of extreme value statistics appear in the Integer Partion/Bose gas problem. The connection between these three different problems respectively in probability theory, number theory and statistical physics is intriguing and fascinating.
Posted by: brunel
Thu
17 Apr 2008
Symmetry-breaking vacua and baryon condensates in AdS/CFT
James Sparks
(Oxford)
Wed
16 Apr 2008
Gluon amplitude/Wilson loop duality
James Drummond
(Annecy)
Abstract:
I will summarise recent developments which indicate that there is a surprising
duality between gluon amplitudes and Wilson loops in supersymmetric Yang-Mills
theory. The motivation for the duality comes from the proposal for the strong
coupling form of gluon amplitudes due to Alday and Maldacena. The evidence that the
duality holds also at weak coupling comes from direct calculations of both objects
and an analysis of a surprising 'dual' conformal symmetry of the gluon amplitudes
which has a natural interpretation for the Wilson loops.
I will summarise recent developments which indicate that there is a surprising
duality between gluon amplitudes and Wilson loops in supersymmetric Yang-Mills
theory. The motivation for the duality comes from the proposal for the strong
coupling form of gluon amplitudes due to Alday and Maldacena. The evidence that the
duality holds also at weak coupling comes from direct calculations of both objects
and an analysis of a surprising 'dual' conformal symmetry of the gluon amplitudes
which has a natural interpretation for the Wilson loops.
Posted by: QMW
Tue
15 Apr 2008
Horseshoe like solutions to the CKP equation
Vladimir Matveev
(Univ. Bourgogne)
Abstract:
The cylindrical Kadomtsev-Petviashvily equation (CKP) also known as Johnson equation was introduced by R.S. Johnson in 1978 in the context of describing surface waves in a shallow imcopressible fluid. Later it was derived also as describing the internal waves in a stratified medium by V.D. Lipowskij in 1995. The same equation was obtained in 2000 for description of nonlinear acoustic waves by S. Leble and A. Sukhov.
We present a large families of explicit solutions to the CKP-I equation and the CKP -II equation obtained by means of the algebrogeometrical approach and by use of the Darboux transformation method. Some plots of these solutions will be also presented as well as the hamiltonian formulation of the CKP model. Particular case of the obtained solutions with crossed parabolic profiles correspond well enough to the real waves observed in thin films of shallow water being cooled along the inclined plane. This talk is based on a recent joint work with A.O Smirnov and Ch. Klein.
The cylindrical Kadomtsev-Petviashvily equation (CKP) also known as Johnson equation was introduced by R.S. Johnson in 1978 in the context of describing surface waves in a shallow imcopressible fluid. Later it was derived also as describing the internal waves in a stratified medium by V.D. Lipowskij in 1995. The same equation was obtained in 2000 for description of nonlinear acoustic waves by S. Leble and A. Sukhov.
We present a large families of explicit solutions to the CKP-I equation and the CKP -II equation obtained by means of the algebrogeometrical approach and by use of the Darboux transformation method. Some plots of these solutions will be also presented as well as the hamiltonian formulation of the CKP model. Particular case of the obtained solutions with crossed parabolic profiles correspond well enough to the real waves observed in thin films of shallow water being cooled along the inclined plane. This talk is based on a recent joint work with A.O Smirnov and Ch. Klein.
Posted by: brunel
Thu
10 Apr 2008
Towards precision physics at TeV colliders
Gudrun Heinrich
(Durham)
Wed
9 Apr 2008
Topological strings in two dimensions and gauge theory
Nikita Nekrasov
(IHES)
Abstract:
First of two lectures. For details, please consult the webpage www.ma.ic.ac.uk (slash) (tilde) rpwt (slash) LMS.html (sorry, triangle server does not allow special characters)
First of two lectures. For details, please consult the webpage www.ma.ic.ac.uk (slash) (tilde) rpwt (slash) LMS.html (sorry, triangle server does not allow special characters)
Posted by: KCL
Tue
8 Apr 2008
Kahler-Einstein and Ricci solitons on toric Fano manifolds
Simon Donaldson
(Imperial College)
Abstract:
For details, please consult the webpage www.ma.ic.ac.uk (slash) (tilde) rpwt (slash) LMS.html
For details, please consult the webpage www.ma.ic.ac.uk (slash) (tilde) rpwt (slash) LMS.html
Posted by: KCL
Tue
8 Apr 2008
Boundaries and Defects in Sine-Gordon Theory
Peter Bowcock
(Durham University)
Abstract:
TBA
TBA
Posted by: KCL
Mon
7 Apr 2008
LMS invited lectures - Random Surfaces
Andrei Okounkov
(Princeton)
Abstract:
2006 Fields medalist Okounkov's invited lecture series begins on Monday.
Ideally only those who registered would come to the first few Okounkov lectures, as the IMS has limited space. Anyone else who wants to come is of course very welcome, but please stand at the back for the first few (oversubscribed) lectures. After that things will thin out and there should be plenty of room.
For details, please consult the webpage www.ma.ic.ac.uk (slash) (tilde) rpwt (slash) LMS.html
(sorry, triangle server does not allow special characters)
2006 Fields medalist Okounkov's invited lecture series begins on Monday.
Ideally only those who registered would come to the first few Okounkov lectures, as the IMS has limited space. Anyone else who wants to come is of course very welcome, but please stand at the back for the first few (oversubscribed) lectures. After that things will thin out and there should be plenty of room.
For details, please consult the webpage www.ma.ic.ac.uk (slash) (tilde) rpwt (slash) LMS.html
(sorry, triangle server does not allow special characters)
Posted by: KCL
Mon
7 Apr 2008
Dimer models and local non-commutative algebraic geometry
Balazs Szendroi
(Oxford)
Abstract:
For details, please consult the webpage www.ma.ic.ac.uk (slash) (tilde) rpwt (slash) LMS.html
For details, please consult the webpage www.ma.ic.ac.uk (slash) (tilde) rpwt (slash) LMS.html
Posted by: KCL
Tue
1 Apr 2008
Making modules into algebras
Jan Grabowski
(Oxford University)
Abstract:
Modules for associative or Lie algebras are just vector spaces acted on by the algebra. This means that we can take the product of an algebra element with a module element in a sensible way. Typically, one cannot take the product of two module elements, though.
However, in certain circumstances, it is possible to make a module into an associative or Lie algebra, in a way that is compatible with the action. I will start with some examples for finite-dimensional Lie algebras, then infinite-dimensional Kac-Moody Lie algebras and finally quantized enveloping algebras. The products we get will turn out to involve braidings, giving us braided Lie algebras and braided enveloping algebras. I will also demonstrate one use for this extra structure, namely gluing together the module and the original algebra to get bigger algebras.
Modules for associative or Lie algebras are just vector spaces acted on by the algebra. This means that we can take the product of an algebra element with a module element in a sensible way. Typically, one cannot take the product of two module elements, though.
However, in certain circumstances, it is possible to make a module into an associative or Lie algebra, in a way that is compatible with the action. I will start with some examples for finite-dimensional Lie algebras, then infinite-dimensional Kac-Moody Lie algebras and finally quantized enveloping algebras. The products we get will turn out to involve braidings, giving us braided Lie algebras and braided enveloping algebras. I will also demonstrate one use for this extra structure, namely gluing together the module and the original algebra to get bigger algebras.
Posted by: KCL
March 2008
Wed
19 Mar 2008
Braneworld black holes
Simon Ross
(Durham)
Abstract:
I will review the problem of constructing black holes on a braneworld with AdS bulk, and the arguments that a full classical 5D solution will correspond to a quantum corrected 4D black hole. I will show that for negative brane cosmological constant, a Schwarzschild-AdS black string in the bulk can be consistently interpreted as a quantum-corrected black hole on the brane, but the form of the quantum corrections is unlike what we would expect.
I will review the problem of constructing black holes on a braneworld with AdS bulk, and the arguments that a full classical 5D solution will correspond to a quantum corrected 4D black hole. I will show that for negative brane cosmological constant, a Schwarzschild-AdS black string in the bulk can be consistently interpreted as a quantum-corrected black hole on the brane, but the form of the quantum corrections is unlike what we would expect.
Posted by: KCL
Wed
19 Mar 2008
Eikonal Methods in AdS/CFT: graviton exchange and the pomeron
Miguel Costa
(University of Porto)
Abstract:
We derive the eikonal approximation to high energy interactions in Anti-de Sitter spacetime, resuming in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant. Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual CFT four point function for small values of cross ratios, in a Lorentzian regime. We explore the consequences of this result to the dual CFT. In the planar limit this Lorentzian amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling. At large coupling, the pole corresponds to graviton exchange in AdS, whereas at weak coupling, the pole is that of the hard perturbative BFKL pomeron. The conformal symmetry of the transverse space E2 is trivially realized on the dual holographic space H3, allowing for a unified description of both weak and strong 't Hooft coupling regimes. The analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation.
We derive the eikonal approximation to high energy interactions in Anti-de Sitter spacetime, resuming in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant. Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual CFT four point function for small values of cross ratios, in a Lorentzian regime. We explore the consequences of this result to the dual CFT. In the planar limit this Lorentzian amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling. At large coupling, the pole corresponds to graviton exchange in AdS, whereas at weak coupling, the pole is that of the hard perturbative BFKL pomeron. The conformal symmetry of the transverse space E2 is trivially realized on the dual holographic space H3, allowing for a unified description of both weak and strong 't Hooft coupling regimes. The analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation.
Posted by: KCL
Tue
18 Mar 2008
Infinite-dimensional diffusions and integrable equations
Pierre van Moerbeke
(Brandeis, USA)
Abstract:
It is shown that non-intersecting Brownian particles, leaving
from one point on the real line and forced to return to one or two points lead to some infinite-dimensional diffusions, which are described by non-linear PDE's. These equations have their origin in the theory of multicomponent KP equations.
It is shown that non-intersecting Brownian particles, leaving
from one point on the real line and forced to return to one or two points lead to some infinite-dimensional diffusions, which are described by non-linear PDE's. These equations have their origin in the theory of multicomponent KP equations.
Posted by: brunel
Fri
14 Mar 2008
Sasaki-Einstein Geometry.
James Sparks
(Oxford University)
Abstract:
Sasakian geometry is the odd-dimensional cousin of Kahler geometry. Although the two are very closely related, there are some interesting differences. I will give an introduction to Sasakian, and in particular Sasaki-Einstein, geometry, and review some of the developments in this subject over the last few years. In particular I'll cover explicit constructions, toric Sasakian geometry, and obstructions. Some of these results also provide new insights into Kahler geometry - for example, I'll describe very simple new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.
Sasakian geometry is the odd-dimensional cousin of Kahler geometry. Although the two are very closely related, there are some interesting differences. I will give an introduction to Sasakian, and in particular Sasaki-Einstein, geometry, and review some of the developments in this subject over the last few years. In particular I'll cover explicit constructions, toric Sasakian geometry, and obstructions. Some of these results also provide new insights into Kahler geometry - for example, I'll describe very simple new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.
Posted by: IC
Thu
13 Mar 2008
Supersymmetry Relations and (N)MHV-Amplitudes in Superstring Theory
Stephan Stieberger
(Munich)
Wed
12 Mar 2008
QCD bound states and AdS/CFT correspondence
📍 London
Konstadinos Siampos
(University of Patras)
Abstract:
I will review the computation of the quark-antiquark potential within the AdS/CFT correspondence. I will explain in detail the conformal case and apply this machinery in more general backgrounds, where multivalued potentials
appear and stability issues have to be considered in order to isolate the physical branches of the potential. Finally I will extend this idea in the case of dyons and baryons. Mechanical analogues of the above configurations will be
given.
I will review the computation of the quark-antiquark potential within the AdS/CFT correspondence. I will explain in detail the conformal case and apply this machinery in more general backgrounds, where multivalued potentials
appear and stability issues have to be considered in order to isolate the physical branches of the potential. Finally I will extend this idea in the case of dyons and baryons. Mechanical analogues of the above configurations will be
given.
Posted by: KCL
Wed
12 Mar 2008
Triadophilia: A Special Corner in the Landscape
Yang-Hui He
(Oxford University)
Abstract:
We point out a special corner in the space of Calabi-Yau compactifications where standard-like models tend to emerge. We show how these scenarios are inter-related via a mathematical process of transgression of bundles, a generalisation of the conifold transition. Perhaps our world is special and we live in this oasis within the multitude of vacua.
We point out a special corner in the space of Calabi-Yau compactifications where standard-like models tend to emerge. We show how these scenarios are inter-related via a mathematical process of transgression of bundles, a generalisation of the conifold transition. Perhaps our world is special and we live in this oasis within the multitude of vacua.
Posted by: IC
Wed
12 Mar 2008
On Brauer diagram categories, representations, and spin-chain spectra
Paul Martin
(Leeds)
Tue
11 Mar 2008
Topological quantum computation from non-abelian anyons
Paul Fendley
(University of Virginia, USA)
Abstract:
I discuss how systems with non-abelian anyons can be used to build a topological quantum computer. Operations are performed by braiding the anyons, because the outcome of braiding is a purely topological property, such quantum computers should be robust against local errors. I will give
several examples of how such anyons arise in fractional quantum Hall systems and in quantum loop models. Mathematical byproducts of this work are algebraic proofs and extensions of Tutte's identities for the chromatic polynomial (the zero-temperature Potts-model partition
function).
I discuss how systems with non-abelian anyons can be used to build a topological quantum computer. Operations are performed by braiding the anyons, because the outcome of braiding is a purely topological property, such quantum computers should be robust against local errors. I will give
several examples of how such anyons arise in fractional quantum Hall systems and in quantum loop models. Mathematical byproducts of this work are algebraic proofs and extensions of Tutte's identities for the chromatic polynomial (the zero-temperature Potts-model partition
function).
Posted by: KCL
Mon
10 Mar 2008
Conformal field theory and Frobenius algebras
Ingo Runkel
(KCL)
Abstract:
Two-dimensional conformal field theory can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. Generalising what one finds for 2d topological field theories, a solution to these constraints can be obtained from a symmetric special Frobenius algebra in the appropriate braided monoidal category.
Two-dimensional conformal field theory can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. Generalising what one finds for 2d topological field theories, a solution to these constraints can be obtained from a symmetric special Frobenius algebra in the appropriate braided monoidal category.
Posted by: IC
Thu
6 Mar 2008
Gauge-Theory Amplitudes from Weak to Strong Coupling
David Kosower
(Saclay)
Wed
5 Mar 2008
A Des Res in the Landscape
📍 London
Philip Candelas
(Oxford)
Wed
5 Mar 2008
Black Hole Near-Horizon Geometries
James Lucietti
(Durham University)
Abstract:
Extremal (especially BPS) black holes are of special importance in string theory and AdS/CFT. Their near-horizon geometries provide a precise tool for investigating certain aspects of such black holes. I will begin with a discussion of some general properties of near-horizon geometries. I will then describe some specific applications of these ideas which will include: a classification of near-horizon geometries of asymptotically AdS(5) supersymmetric black holes with two rotational symmetries (of relevance to AdS/CFT), a proof of symmetry enhancement of generic near-horizon geometries in D=4,5 (of relevance to the attractor mechanism), near-horizon geometries in D greater than 5 and finally some open problems.
Extremal (especially BPS) black holes are of special importance in string theory and AdS/CFT. Their near-horizon geometries provide a precise tool for investigating certain aspects of such black holes. I will begin with a discussion of some general properties of near-horizon geometries. I will then describe some specific applications of these ideas which will include: a classification of near-horizon geometries of asymptotically AdS(5) supersymmetric black holes with two rotational symmetries (of relevance to AdS/CFT), a proof of symmetry enhancement of generic near-horizon geometries in D=4,5 (of relevance to the attractor mechanism), near-horizon geometries in D greater than 5 and finally some open problems.
Posted by: IC
Tue
4 Mar 2008
Seeing Through the String Landscape: Domain Walls and Black Holes
Dieter Luest
(Munich)
Tue
4 Mar 2008
Homology and Fugue
William Turner
(Oxford University)
Abstract:
We discuss the possibility of applying modern techniques of homological algebra to the composition and analysis of fugues.
We discuss the possibility of applying modern techniques of homological algebra to the composition and analysis of fugues.
Posted by: KCL
Mon
3 Mar 2008
Combinatorial Floer homology
Ciprian Manolescu
(Columbia)
February 2008
Thu
28 Feb 2008
Geometry of the standard model and neutrino mass terms
John Barrett
(Nottingham)
Wed
27 Feb 2008
Killing superalgebras in supergravity
Jose Figueroa-O'Farrill
(University of Edinburgh)
Abstract:
I will discuss several constructions of superalgebras associated to the Killing spinors of a supergravity background, with special emphasis on the ten- and eleven-dimensional supergravities.
I will discuss several constructions of superalgebras associated to the Killing spinors of a supergravity background, with special emphasis on the ten- and eleven-dimensional supergravities.
Posted by: KCL
Wed
27 Feb 2008
Improved Holographic QCD
Elias Kiritsis
(Ecole Polytechnique, CPHT)
Abstract:
Various holographic approaches to QCD in five dimensions are explored using input both from the perturbative five-dimensional non-critical string theory as well as QCD. It is argued that a gravity theory in five dimensions coupled to a dilaton and an axion may capture the important qualitative features of pure YM theory. A part of the effects of higher a'-corrections is resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact beta-function of QCD, and its knowledge determines the full structure of the vacuum solution. The geometry near the UV boundary is that of AdS5 with logarithmic corrections reflecting the asymptotic freedom of QCD. The IR confining geometries are classified and analyzed. Near the singularity the 't Hooft coupling is driven to infinity. The glueball spectra are gapped and discrete, and they favorably compare to the lattice data. Quite generally, confinement and discrete spectra imply each other. Asymptotically linear glueball masses can also be achieved. Asymptotic mass ratios of various glueballs with different spin also turn out to be universal. Meson dynamics is implemented via space filling D4-anti D4 brane pairs. The associated tachyon dynamics is analyzed and chiral symmetry breaking is shown. The dynamics of the RR axion is analyzed, and the non-perturbative running of the QCD theta-angle is obtained. It is shown to always vanish in the IR. The finite temperature structure is also analyzed and phase diagram is studied. Our preliminary results show a first order deconfining transition to a QGP phase with a transition temperature in agreement with lattice data.
Various holographic approaches to QCD in five dimensions are explored using input both from the perturbative five-dimensional non-critical string theory as well as QCD. It is argued that a gravity theory in five dimensions coupled to a dilaton and an axion may capture the important qualitative features of pure YM theory. A part of the effects of higher a'-corrections is resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact beta-function of QCD, and its knowledge determines the full structure of the vacuum solution. The geometry near the UV boundary is that of AdS5 with logarithmic corrections reflecting the asymptotic freedom of QCD. The IR confining geometries are classified and analyzed. Near the singularity the 't Hooft coupling is driven to infinity. The glueball spectra are gapped and discrete, and they favorably compare to the lattice data. Quite generally, confinement and discrete spectra imply each other. Asymptotically linear glueball masses can also be achieved. Asymptotic mass ratios of various glueballs with different spin also turn out to be universal. Meson dynamics is implemented via space filling D4-anti D4 brane pairs. The associated tachyon dynamics is analyzed and chiral symmetry breaking is shown. The dynamics of the RR axion is analyzed, and the non-perturbative running of the QCD theta-angle is obtained. It is shown to always vanish in the IR. The finite temperature structure is also analyzed and phase diagram is studied. Our preliminary results show a first order deconfining transition to a QGP phase with a transition temperature in agreement with lattice data.
Posted by: KCL
Tue
26 Feb 2008
Quantum Ergodicity of Graphs
Fabien Piotet
(Bristol)
Abstract:
Quantum graphs have become a paradigm for quantum chaos. It is indeed known that universal interference effects can be observed in the statistics of their spectra. Here, we investigate the possibility for the modulus of the high energy eigenfunctions to become uniformly spread over the graph - a property known as quantum ergodicity. A field
theoretical method enables to identify the class of quantum ergodic graphs, and to predict the rate with which quantum ergodicity is obtained.
Quantum graphs have become a paradigm for quantum chaos. It is indeed known that universal interference effects can be observed in the statistics of their spectra. Here, we investigate the possibility for the modulus of the high energy eigenfunctions to become uniformly spread over the graph - a property known as quantum ergodicity. A field
theoretical method enables to identify the class of quantum ergodic graphs, and to predict the rate with which quantum ergodicity is obtained.
Posted by: brunel
Tue
26 Feb 2008
Calogero model on a star graph
Nicolas Crampe
(International School for Advanced Studies, Trieste, Italy)
Abstract:
This seminar deals with integrable models on graphs. After some
motivations for studying such systems, I give the proof of the integrability of
a Calogero model on a star graph (see J.Phys. A 40 (2007) 5491 and
math-ph/0609057). I also discuss its symmetry. In particular, I emphasise the links
with the complex reflection groups and twisted algebra. I finish with
open problems in this quite recent domain of integrable models.
This seminar deals with integrable models on graphs. After some
motivations for studying such systems, I give the proof of the integrability of
a Calogero model on a star graph (see J.Phys. A 40 (2007) 5491 and
math-ph/0609057). I also discuss its symmetry. In particular, I emphasise the links
with the complex reflection groups and twisted algebra. I finish with
open problems in this quite recent domain of integrable models.
Posted by: KCL
Mon
25 Feb 2008
Counting curves in Calabi-Yau 3-folds, part 3
Richard Thomas
(Imperial College)
Abstract:
These will be introductory lectures surveying GW, MNOP and GV invariants – all different ways of counting curves.
For a string theorist this involves seeing the curve as, respectively, the world sheet of a string, a D-brane, or a BPS thingummy.
I will describe a 4th way via stable pairs, which in effect means counting D-branes (or stable objects of the derived category, to mathematicians) after a change of stability condition.
These will be introductory lectures surveying GW, MNOP and GV invariants – all different ways of counting curves.
For a string theorist this involves seeing the curve as, respectively, the world sheet of a string, a D-brane, or a BPS thingummy.
I will describe a 4th way via stable pairs, which in effect means counting D-branes (or stable objects of the derived category, to mathematicians) after a change of stability condition.
Posted by: IC
Wed
20 Feb 2008
Real forms of complex higher-spin field equations and new exact solutions
📍 London
Carlo Iazeolla
(Pisa)
Wed
20 Feb 2008
Large Extremal Black Holes in AdS5
Sangmin Lee
(Seoul National University)
Abstract:
We study the near horizon geometry of extremal black holes in five dimensional gauged supergravity using Sen's entropy function formalism. Special attention is paid to the large black hole limit where the near horizon solution exhibits a universal dependence on the rotation. The physical properties of the large black hole solution are shown to agree with predictions from fluid mechanical description of the dual conformal field theory.
We study the near horizon geometry of extremal black holes in five dimensional gauged supergravity using Sen's entropy function formalism. Special attention is paid to the large black hole limit where the near horizon solution exhibits a universal dependence on the rotation. The physical properties of the large black hole solution are shown to agree with predictions from fluid mechanical description of the dual conformal field theory.
Posted by: IC
Tue
19 Feb 2008
Real forms of complex higher-spin field equations and new exact solutions
Carlo Iazeolla
(Pisa)
Tue
19 Feb 2008
Reflection Equation and deformation quantization
Andrey Mudrov
(Leicester University)
Abstract:
Reflection equation or boundary Yang-Baxter equation is an important object in the theory
of quantum groups and integrable models, along with the famous RTT relation. In my talk I focus on the role of the related algebraic structures in the deformation quantization. We provide a survey of their basic
properties from a geometric point of view.
Reflection equation or boundary Yang-Baxter equation is an important object in the theory
of quantum groups and integrable models, along with the famous RTT relation. In my talk I focus on the role of the related algebraic structures in the deformation quantization. We provide a survey of their basic
properties from a geometric point of view.
Posted by: KCL
Mon
18 Feb 2008
L_oo algebra connections and application to String- and Chern-Simons n-Transport
Urs Schreiber
(Hamburg)
Abstract:
We conceive higher bundles with connections entirely Lie algebraically by, essentially, extending the Cartan-Ehresmann definition of a connection from Lie algebras to L-infinity algebras. Using this machinery, we study Chern-Simons n-bundles as obstructions to lifts through String-like extensions of L-infinity algebras.
We conceive higher bundles with connections entirely Lie algebraically by, essentially, extending the Cartan-Ehresmann definition of a connection from Lie algebras to L-infinity algebras. Using this machinery, we study Chern-Simons n-bundles as obstructions to lifts through String-like extensions of L-infinity algebras.
Posted by: IC
Thu
14 Feb 2008
The plethystic program
Yang Hui He
(Oxford)
Wed
13 Feb 2008
Supersymmetry and the Berry Phase of Branes
Julian Sonner
(Cambridge University)
Abstract:
In this talk I want to describe recent work on geometric (Berry) phases that arise in the quantum theory of certain D-brane states. After briefly reviewing the geometric phase in general theories, I will turn to supersymmetric systems of the type arising in D0-brane configurations in string theory. Interestingly, the resulting Berry phases are related to the four Hopf fibrations. I will show how this fact arises as a consequence of the close relationship between SUSY and the division algebras. The framework of string theory allows to draw some interesting physical consequences from these Berry phases, such as a new interpretation of the Berry phase in terms of gravitational precession and the surprising result that in certain configurations, D0 branes behave as anyons.
In this talk I want to describe recent work on geometric (Berry) phases that arise in the quantum theory of certain D-brane states. After briefly reviewing the geometric phase in general theories, I will turn to supersymmetric systems of the type arising in D0-brane configurations in string theory. Interestingly, the resulting Berry phases are related to the four Hopf fibrations. I will show how this fact arises as a consequence of the close relationship between SUSY and the division algebras. The framework of string theory allows to draw some interesting physical consequences from these Berry phases, such as a new interpretation of the Berry phase in terms of gravitational precession and the surprising result that in certain configurations, D0 branes behave as anyons.
Posted by: IC
Wed
13 Feb 2008
LARGE volume string compactifications
📍 London
Fernando Quevedo
(DAMTP)
Tue
12 Feb 2008
Aspects of purely transmitting defects in integrable field theories
Ed Corrigan
(University of York)
Abstract:
An integrable shock, or discontinuity, is a type of 'defect' allowed, in the sense of not destroying the property of integrability, within (at least some) integrable field theories. A main example is the sine-Gordon model, or, more generally, the a-series of affine Toda field theories. Such 'defects' have interesting properties in the classical and quantum domains especially with regard to their interactions with solitons - or indeed with each other, if there is more than one of them and they are allowed to move. This talk will present a survey of recent results and describe some open problems.
An integrable shock, or discontinuity, is a type of 'defect' allowed, in the sense of not destroying the property of integrability, within (at least some) integrable field theories. A main example is the sine-Gordon model, or, more generally, the a-series of affine Toda field theories. Such 'defects' have interesting properties in the classical and quantum domains especially with regard to their interactions with solitons - or indeed with each other, if there is more than one of them and they are allowed to move. This talk will present a survey of recent results and describe some open problems.
Posted by: KCL
Mon
11 Feb 2008
Counting curves in Calabi-Yau 3-folds, part 2
Richard Thomas
(Imperial College)
Abstract:
These will be introductory lectures surveying GW, MNOP and GV invariants - all different ways of counting curves.
For a string theorist this involves seeing the curve as, respectively, the world sheet of a string, a D-brane, or a BPS thingummy.
I will describe a 4th way via stable pairs, which in effect means counting D-branes (or stable objects of the derived category, to mathematicians) after a change of stability condition.
These will be introductory lectures surveying GW, MNOP and GV invariants - all different ways of counting curves.
For a string theorist this involves seeing the curve as, respectively, the world sheet of a string, a D-brane, or a BPS thingummy.
I will describe a 4th way via stable pairs, which in effect means counting D-branes (or stable objects of the derived category, to mathematicians) after a change of stability condition.
Posted by: IC
Wed
6 Feb 2008
The Superconformal Index and q-Series: New Tests of N=1 Dualities
Francis Dolan
(DIAS and Univ. of Southampton)
Abstract:
Recently Romelsberger made some conjectures about an index for N=1 superconformal quantum field theories applied to certain Seiberg dual theories. Recent joint work by me and Hugh Osborn proves and extends these conjectures by employing certain q-series type identities. I will discuss the superconformal index, how it applies for more general N=1 dual theories and, briefly, the proof of these conjectures.
Recently Romelsberger made some conjectures about an index for N=1 superconformal quantum field theories applied to certain Seiberg dual theories. Recent joint work by me and Hugh Osborn proves and extends these conjectures by employing certain q-series type identities. I will discuss the superconformal index, how it applies for more general N=1 dual theories and, briefly, the proof of these conjectures.
Posted by: IC
Wed
6 Feb 2008
Pohlmeyer reduction of AdS(5) x S5 superstring sigma model
📍 London
Arkady Tseytlin
(Imperial college)
Tue
5 Feb 2008
From Amplitudes to Wilson Loops and Holography
Andreas Brandhuber
(Queen Mary)
Tue
5 Feb 2008
Pohlmeyer reduction of AdS(5) x S5 superstring sigma model
Arkady Tseytlin
(Imperial College London)
Abstract:
Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS_5 x S 5 superstring world-sheet theory in terms of physical degrees of freedom we construct a Pohlmeyer-reduced version of the corresponding sigma model. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gauge-fixed equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW-model with an integrable potential coupled also to a set of 2d fermionic fields.
We show that in the special case of the AdS_2 x S2 superstring model the reduced theory is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.
Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS_5 x S 5 superstring world-sheet theory in terms of physical degrees of freedom we construct a Pohlmeyer-reduced version of the corresponding sigma model. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gauge-fixed equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW-model with an integrable potential coupled also to a set of 2d fermionic fields.
We show that in the special case of the AdS_2 x S2 superstring model the reduced theory is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.
Posted by: KCL
Mon
4 Feb 2008
Batalin-Vilkovisky algebras, topological gravity, Hodge theory, Kodaira-Spencer field theory and intersection theory on Deligne-Mumford moduli spaces
Ezra Getzler
(IMS and Northwestern University)
Abstract:
I give an outline of the program of Shadrin and his collaborators, to give explicit formulas for correlators in topological gravity (with descendants), starting with a Batalin-Vilkovisky algebra. In particular, I will try to explain the relationship with Givental's work on Gromov-Witten invariants. No background is assumed.
I give an outline of the program of Shadrin and his collaborators, to give explicit formulas for correlators in topological gravity (with descendants), starting with a Batalin-Vilkovisky algebra. In particular, I will try to explain the relationship with Givental's work on Gromov-Witten invariants. No background is assumed.
Posted by: IC
Mon
4 Feb 2008
Infrared and collinear dynamics in massless gauge theories
Lorenzo Magnea
(Universita' di Torino)
Abstract:
This is the first of three lectures: see the Graduate Program webpage at http://www.strings.ph.qmw.ac.uk/ for more information.
This is the first of three lectures: see the Graduate Program webpage at http://www.strings.ph.qmw.ac.uk/ for more information.
Posted by: QMW
January 2008
Wed
30 Jan 2008
Dyon Death Eaters
📍 London
Sunil Mukhi
(Tata Institute)
Abstract:
I will describe and analyse general two-body decays of primitive and non-primitive 1/4-BPS dyons in four-dimensional type IIB string compactifications. For half-BPS decays, a relation is found between walls of marginal stability and the mathematics of Farey sequences and Ford circles. The relationship of marginal decay to the breakup of multi-centred dyons will also be discussed.
I will describe and analyse general two-body decays of primitive and non-primitive 1/4-BPS dyons in four-dimensional type IIB string compactifications. For half-BPS decays, a relation is found between walls of marginal stability and the mathematics of Farey sequences and Ford circles. The relationship of marginal decay to the breakup of multi-centred dyons will also be discussed.
Posted by: IC
Wed
30 Jan 2008
Instanton effects from open strings and D-branes
📍 London
Alberto Lerda
(Piemonte Orientale U., Alessandria)
Abstract:
We discuss how non-perturbative instanton effects in supersymmetric gauge theories can be described using open strings and D-branes. We analyse ordinary gauge instantons as well as novel 'exhotic instanton' configurations of purely stringy nature, and discuss their applications and effets in the low-energy effective theory.
We discuss how non-perturbative instanton effects in supersymmetric gauge theories can be described using open strings and D-branes. We analyse ordinary gauge instantons as well as novel 'exhotic instanton' configurations of purely stringy nature, and discuss their applications and effets in the low-energy effective theory.
Posted by: KCL
Tue
29 Jan 2008
RMT, QCD and a mapping theorem through superbosonisation
Francesco Basile
(Brunel/Pisa)
Tue
29 Jan 2008
Rhombus tilings in representation theory
Joseph Chuang
(City University London)
Abstract:
I'll introduce a combinatorial problem on tilings of the plane by rhombi and explain how the solution is related to the representation theory of groups.
I'll introduce a combinatorial problem on tilings of the plane by rhombi and explain how the solution is related to the representation theory of groups.
Posted by: KCL
Mon
28 Jan 2008
Counting curves in Calabi-Yau 3-folds
Richard Thomas
(Imperial College)
Abstract:
These will be introductory lectures surveying GW, MNOP and GV invariants – all different ways of counting curves.
For a string theorist this involves seeing the curve as, respectively, the world sheet of a string, a D-brane, or a BPS thingummy.
I will describe a 4th way via stable pairs, which in effect means counting D-branes (or stable objects of the derived category, to mathematicians) after a change of stability condition.
These will be introductory lectures surveying GW, MNOP and GV invariants – all different ways of counting curves.
For a string theorist this involves seeing the curve as, respectively, the world sheet of a string, a D-brane, or a BPS thingummy.
I will describe a 4th way via stable pairs, which in effect means counting D-branes (or stable objects of the derived category, to mathematicians) after a change of stability condition.
Posted by: IC
Thu
24 Jan 2008
E11 extended spacetime and gauged supergravities
Fabio Riccioni
(KCL)
Wed
23 Jan 2008
D3-Branes Probing Singularities
📍 London
Edward Segal
(Imperial College)
Abstract:
I'll discuss (from a mathematician's perspective) the process of extracting an effective quiver gauge theory from a D3-brane probing a singularity in a Calabi-Yau 3-fold.
I'll discuss (from a mathematician's perspective) the process of extracting an effective quiver gauge theory from a D3-brane probing a singularity in a Calabi-Yau 3-fold.
Posted by: KCL
Wed
23 Jan 2008
Looking for higher dimensional droplets in AdS5 x S5
Aristomenis Donos
(DESY)
Abstract:
We will discuss the properties of geometries dual to BPS states of N=4 supersymmetric Yang-Mills theory. Despite the non-linearity of the problem, we develop a universal bubbling AdS description of these geometries by focusing on the boundary conditions which ensure their regularity. In the 1/8 BPS case, we find that the S3 cycle shrinks to zero size on a five-dimensional locus inside the six-dimensional base. Enforcing regularity of the full solution requires that the interior of a smooth, generally disconnected five-dimensional surface be removed from the base. The AdS5 x S5 ground state corresponds to excising the interior of an S5, while the 1/8 BPS excitations correspond to deformations (including topology change) of the S5 and/or the excision of additional droplets from the base.
We will discuss the properties of geometries dual to BPS states of N=4 supersymmetric Yang-Mills theory. Despite the non-linearity of the problem, we develop a universal bubbling AdS description of these geometries by focusing on the boundary conditions which ensure their regularity. In the 1/8 BPS case, we find that the S3 cycle shrinks to zero size on a five-dimensional locus inside the six-dimensional base. Enforcing regularity of the full solution requires that the interior of a smooth, generally disconnected five-dimensional surface be removed from the base. The AdS5 x S5 ground state corresponds to excising the interior of an S5, while the 1/8 BPS excitations correspond to deformations (including topology change) of the S5 and/or the excision of additional droplets from the base.
Posted by: IC
Mon
21 Jan 2008
Supersymmetric AdS solutions and new Kahler geometry
Nakwoo Kim
(Kyung Hee University)
Abstract:
The study of supersymmetric solutions in supergravity have provided invaluable insight into quantum gravity via AdS/CFT correspondence. In this talk I present a new class of intriguing Kahler geometry which appears in the study of AdS solutions from D3 and M2-branes wrapped on 2-cycles. Solving the master equation, which has higher-order couplings in Ricci tensor, we obtain new AdS solutions.
The study of supersymmetric solutions in supergravity have provided invaluable insight into quantum gravity via AdS/CFT correspondence. In this talk I present a new class of intriguing Kahler geometry which appears in the study of AdS solutions from D3 and M2-branes wrapped on 2-cycles. Solving the master equation, which has higher-order couplings in Ricci tensor, we obtain new AdS solutions.
Posted by: IC
Fri
18 Jan 2008
The master space of N=1 gauge theories
Alberto Zaffaroni
(Milano (Bicocca) and INFN)
Abstract:
I discuss some aspects of the full moduli space of N=1
supersymmetric gauge theories, focusing on those arising on D-branes at Calabi-Yau singularities. Of particola importance is the full moduli space for one brane, called the master space. I discuss its geometrical properties and its relation with the uncovering of hidden symmetries and the counting of BPS states of the gauge theory.
I discuss some aspects of the full moduli space of N=1
supersymmetric gauge theories, focusing on those arising on D-branes at Calabi-Yau singularities. Of particola importance is the full moduli space for one brane, called the master space. I discuss its geometrical properties and its relation with the uncovering of hidden symmetries and the counting of BPS states of the gauge theory.
Posted by: IC
Wed
16 Jan 2008
The Homogeneous and Symmetric Space Sine-Gordon Models: a Review
Olalla Castro Alvaredo
(City University London)
Abstract:
The homogeneous and symmetric space sine-Gordon models (HSG- and SSSG-models, for short) are two groups of two-dimensional integrable quantum field theories which belong to a larger class of models: the non-Abelian affine Toda field theories.
In this talk I intend to review the main results known up to date about these two classes of models, paying special attention to my own contributions to the subject. These contributions have focused on the one hand, on the development of the bootstrap program for the HSG-models (TBA-analysis, computation of form factors and correlation functions etc) and, on the other hand, on the study of the quantum integrability and spectrum of a subset of the SSSG-models, known as split models.
The homogeneous and symmetric space sine-Gordon models (HSG- and SSSG-models, for short) are two groups of two-dimensional integrable quantum field theories which belong to a larger class of models: the non-Abelian affine Toda field theories.
In this talk I intend to review the main results known up to date about these two classes of models, paying special attention to my own contributions to the subject. These contributions have focused on the one hand, on the development of the bootstrap program for the HSG-models (TBA-analysis, computation of form factors and correlation functions etc) and, on the other hand, on the study of the quantum integrability and spectrum of a subset of the SSSG-models, known as split models.
Posted by: IC