Triangle Seminars
December 2007
Tue
11 Dec 2007
NonHermitian Random Matrix Theory and its Applications
Gernot Akemann
(Brunel University West London)
Abstract:
Random Matrix Theory (RMT) has many applications in Physics and other Sciences. The starting point is given by the global symmetries of the underlying Hamiltonian or other relevant operator of the theory to be described. In this talk I will focus on the so-called chiral ensembles and their complex extensions, generalising the Wigner-Dyson classes that were first introduced. The corresponding Gaussian RMT with NxN matrices can be solved exactly using Laguerre Polynomials, both for matrices with real and complex eigenvalues. An example where these find applications are the spectra of Dirac operators in Lattice Gauge Theory.
Random Matrix Theory (RMT) has many applications in Physics and other Sciences. The starting point is given by the global symmetries of the underlying Hamiltonian or other relevant operator of the theory to be described. In this talk I will focus on the so-called chiral ensembles and their complex extensions, generalising the Wigner-Dyson classes that were first introduced. The corresponding Gaussian RMT with NxN matrices can be solved exactly using Laguerre Polynomials, both for matrices with real and complex eigenvalues. An example where these find applications are the spectra of Dirac operators in Lattice Gauge Theory.
Posted by: KCL
Thu
6 Dec 2007
Infinite-Dimensional Symmetries of Two-Dimensional Coset Models Coupled to Gravity
Christopher Pope
(Texas A and M University)
Abstract:
The global symmetry groups that result from compactifying eleven-dimensional supergravity on an n-dimensional torus play a central role in our understanding of U-dualities in string and M-theory. The mechanism leading to the En Lie algebra upon compactification on Tn is well-known for n less than 9, but the situation for n=9, corresponding to the compactification to 2 dimensions, has been described much less clearly in the literature. We give an elementary, and completely explicit, description of the infinite-dimensional symmetries of all symmetric-space coset models in 2-dimensional gravitational backgrounds, including symmetries of both Kac-Moody and Virasoro type.
The global symmetry groups that result from compactifying eleven-dimensional supergravity on an n-dimensional torus play a central role in our understanding of U-dualities in string and M-theory. The mechanism leading to the En Lie algebra upon compactification on Tn is well-known for n less than 9, but the situation for n=9, corresponding to the compactification to 2 dimensions, has been described much less clearly in the literature. We give an elementary, and completely explicit, description of the infinite-dimensional symmetries of all symmetric-space coset models in 2-dimensional gravitational backgrounds, including symmetries of both Kac-Moody and Virasoro type.
Posted by: IC
Wed
5 Dec 2007
New Connections between Topological String Theory and Matrix Models
Albrecht Klemm
(Univ. of Bonn)
Abstract:
We explain the relation between the holomorphic anomaly equations in topological string theory and the loop equations in matrix models. We explain a strategy for their solutions using modular forms, which applies to open and closed topological string theory on (non) compact Calabi-Yau manifolds. (A description how to find Lecture Theatre 1 is given on http://brahms.mth.kcl.ac.uk/cgi-bin/main.pl?action=triangle)
We explain the relation between the holomorphic anomaly equations in topological string theory and the loop equations in matrix models. We explain a strategy for their solutions using modular forms, which applies to open and closed topological string theory on (non) compact Calabi-Yau manifolds. (A description how to find Lecture Theatre 1 is given on http://brahms.mth.kcl.ac.uk/cgi-bin/main.pl?action=triangle)
Posted by: KCL
Wed
5 Dec 2007
Wrapping interactions in gauge theory and finite size effects in string theory
Romuald Janik
(Jagellonian University)
Abstract:
Anomalous dimensions of long operators in SYM are described by the asymptotic Bethe ansatz. There exist, in addition, finite size effects due to wrapping interactions. In this talk I would like to argue that within the AdS/CFT correspondence these additional wrapping interactions
are described by finite size corrections in the relevant integrable quantum field theory and analyze the finite size corrections to the giant magnon.
Anomalous dimensions of long operators in SYM are described by the asymptotic Bethe ansatz. There exist, in addition, finite size effects due to wrapping interactions. In this talk I would like to argue that within the AdS/CFT correspondence these additional wrapping interactions
are described by finite size corrections in the relevant integrable quantum field theory and analyze the finite size corrections to the giant magnon.
Posted by: KCL
Tue
4 Dec 2007
Generalized Renewal Process and Imperfect Repair
Maxim Finkelstein
(University of the FreeState, Bloemfontein, South Africa)
Tue
4 Dec 2007
Superstatistics: Theory and Applications
Christian Beck
(Queen Mary)
November 2007
Wed
28 Nov 2007
Physical and Mathematical Challenges of AdS/CFT Integrability
📍 London
Matthias Staudacher
(Potsdam)
Wed
28 Nov 2007
Generalized Kahler Potentials for Supergravity
Nick Halmagyi
(Chicago University, EFI)
Abstract:
I will discuss the targetspace manifestation of the most general (2,2) sigma models with H flux, these include chiral, twisted chiral and semi chiral superfields. I will describe the appearance of a generalized Kahler potential and also outline the use of the deformation space of generalized complex structures in supergravity.
I will discuss the targetspace manifestation of the most general (2,2) sigma models with H flux, these include chiral, twisted chiral and semi chiral superfields. I will describe the appearance of a generalized Kahler potential and also outline the use of the deformation space of generalized complex structures in supergravity.
Posted by: IC
Wed
28 Nov 2007
Representation theory and integrable spin chains
Petr Kulish
(St.Petersburg Department of Steklov Institute of Mathematics)
Abstract:
Solution of the Heisenberg spin chain s=1/2 (spectrum of the energy operator and its eigenvectors) is related with three algebras: the Lie algebra sl(2), group algebra of symmetric group S_N and an infinite dimentional Hopf algebra, Yangian Y(sl(2)). Using representaions of these algebras there are generalization of this model to higher spins s=1, 3/2, 2,
...However there is also possibility to geberalize these algebras preserving structure of their representations. In particular the group algebra of S_N will be substituted by the Temperle – Lieb algebra.
Solution of the Heisenberg spin chain s=1/2 (spectrum of the energy operator and its eigenvectors) is related with three algebras: the Lie algebra sl(2), group algebra of symmetric group S_N and an infinite dimentional Hopf algebra, Yangian Y(sl(2)). Using representaions of these algebras there are generalization of this model to higher spins s=1, 3/2, 2,
...However there is also possibility to geberalize these algebras preserving structure of their representations. In particular the group algebra of S_N will be substituted by the Temperle – Lieb algebra.
Posted by: KCL
Tue
27 Nov 2007
The vertex operator approach to dynamical structure functions
Robert Weston
(Hariot-Watt University, Edinburgh)
Abstract:
I shall present a review of the vertex operator approach to solvable lattice models. I shall briefly describe how this technique is being applied to the computation of dynamical structure functions - the latter being directly assessable via neutron scattering experiments.
I shall present a review of the vertex operator approach to solvable lattice models. I shall briefly describe how this technique is being applied to the computation of dynamical structure functions - the latter being directly assessable via neutron scattering experiments.
Posted by: KCL
Tue
27 Nov 2007
On the top eigenvalue and density of states of heavy tailed random matrices: theory and comparison to financial data
Giulio Biroli
(CEA Saclay)
Fri
23 Nov 2007
Stringy Cosmologies
Nick Toumbas
Thu
22 Nov 2007
Low-energy supersymmetry from non-geometric flux compactifications
Eran Palti
(Oxford)
Wed
21 Nov 2007
Symmetries and defects in conformal field theory
📍 London
Ingo Runkel
(KCL)
Abstract:
Given two conformal field theories, one of which is defined on the upper half plane and the other on the lower half plane, one can ask for conformally invariant ways to join them along the real line. The resulting interface is called a defect line. These defects contain interesting information about the CFT, such as its symmetries, order-disorder dualities and T-dualities. They also provide relations between string theories on different target spaces.
Given two conformal field theories, one of which is defined on the upper half plane and the other on the lower half plane, one can ask for conformally invariant ways to join them along the real line. The resulting interface is called a defect line. These defects contain interesting information about the CFT, such as its symmetries, order-disorder dualities and T-dualities. They also provide relations between string theories on different target spaces.
Posted by: KCL
Wed
21 Nov 2007
Absence of Gravitational Corrections to the Running Gauge Coupling
Jan Plefka
(Humboldt Universitaet, Berlin)
Abstract:
The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this talk we present an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one-loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. This settles the previously open question of a potential regularization scheme dependence of the one-loop beta-function traditionally computed in the background field approach. Furthermore, we show that the remaining logarithmic divergencies give rise to an effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six.
The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this talk we present an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one-loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. This settles the previously open question of a potential regularization scheme dependence of the one-loop beta-function traditionally computed in the background field approach. Furthermore, we show that the remaining logarithmic divergencies give rise to an effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six.
Posted by: IC
Tue
20 Nov 2007
Topological branes and matrix factorisations
Andreas Recknagel
(King's College London)
Abstract:
D-branes in Calabi-Yau manifolds are interesting objects from the point of view of string phenomenology and of pure mathematics, and they have been studied using a conformal field theory as well as geometric methods. In the past few years, a new tool has emerged in the form of matrix factorisations of Landau-Ginzburg potentials, which gives a rather efficient computational handle on the properties of topological Calabi-Yau branes. I will try to give an overview of some of these developments.
D-branes in Calabi-Yau manifolds are interesting objects from the point of view of string phenomenology and of pure mathematics, and they have been studied using a conformal field theory as well as geometric methods. In the past few years, a new tool has emerged in the form of matrix factorisations of Landau-Ginzburg potentials, which gives a rather efficient computational handle on the properties of topological Calabi-Yau branes. I will try to give an overview of some of these developments.
Posted by: KCL
Tue
20 Nov 2007
Modified Landau Gauge on a Lattice-XY Model: Gribov copies, Neuberger problem, Algebraic Geometry and Numerical Algebraic Geometry
Dhagash Mehta
(Adelaide)
Abstract:
Standard nonperturbative covariant gauge fixing procedure leaves the theory with Gribov copies and on lattice even Neuberger zero-zero problem. Due to this Neuberger problem, BRST and SUSY on lattice are still open and urgent questions to be addressed. I will introduce the problems using Landau gauge
for a simple toy model, compact QED on a one dimensional lattice, and propose a modification which completely resolves Gribov-Neuberger problems on this simple toy model
and even the higher dimensional generalization. This gauge-fixing term for compact QED on lattice is the classical XY-model Hamiltonian, and in condensed matter terms the problem is to get ALL extrema of this Hamiltonian exactly. To
give a full analytical proof for the higher dimensional generalization, I will need to introduce a tailor-made terminology of Algebraic Geometry. I will also go on proposing two algorithms for gauge-fixing on lattice that use
sophisticated applied mathematics and give efficient results derived from Numerical Algebraic Geometry.
Standard nonperturbative covariant gauge fixing procedure leaves the theory with Gribov copies and on lattice even Neuberger zero-zero problem. Due to this Neuberger problem, BRST and SUSY on lattice are still open and urgent questions to be addressed. I will introduce the problems using Landau gauge
for a simple toy model, compact QED on a one dimensional lattice, and propose a modification which completely resolves Gribov-Neuberger problems on this simple toy model
and even the higher dimensional generalization. This gauge-fixing term for compact QED on lattice is the classical XY-model Hamiltonian, and in condensed matter terms the problem is to get ALL extrema of this Hamiltonian exactly. To
give a full analytical proof for the higher dimensional generalization, I will need to introduce a tailor-made terminology of Algebraic Geometry. I will also go on proposing two algorithms for gauge-fixing on lattice that use
sophisticated applied mathematics and give efficient results derived from Numerical Algebraic Geometry.
Posted by: brunel
Mon
19 Nov 2007
Open/closed topological field theory and topological gravity
Ezra Getzler
Fri
16 Nov 2007
Heavy Ion Collisions and AdS/CFT
Amos Yarom
(LMU, Munich)
Abstract:
Heavy-ion collision experiments manage to probe the quark-gluon plasma of QCD. The plasma created is strongly coupled and is difficult to analyze using conventional means. In this talk, we shall use the AdS/CFT correspondence to study properties of particles moving through a quark-gluon plasma. Such probe particles provide a model for understanding several unanswered puzzles exhibited by the experiment.
Heavy-ion collision experiments manage to probe the quark-gluon plasma of QCD. The plasma created is strongly coupled and is difficult to analyze using conventional means. In this talk, we shall use the AdS/CFT correspondence to study properties of particles moving through a quark-gluon plasma. Such probe particles provide a model for understanding several unanswered puzzles exhibited by the experiment.
Posted by: IC
Wed
14 Nov 2007
Pohlmeyer reduction of the AdS5 x S5 superstring sigma model
Maxim Grigoriev
(Institute of Mathematical Sciences, Imperial College)
Abstract:
Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS5 x S5 superstring world-sheet theory in terms of physical degrees of freedom we investigate a Pohlmeyer-reduced version of the corresponding supercoset sigma model. The Pohlmeyer reduction procedure involves several steps. 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. The final form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. Its small-fluctuation spectrum is that of 8 bosonic and 8 fermionic degrees of freedom with equal masses. We show that in the special case of the AdS2 x S2 superstring model the reduced theory is supersymmetric: it is equivalent to the (2,2) supersymmetric extension of the sine-Gordon model.
Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS5 x S5 superstring world-sheet theory in terms of physical degrees of freedom we investigate a Pohlmeyer-reduced version of the corresponding supercoset sigma model. The Pohlmeyer reduction procedure involves several steps. 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. The final form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. Its small-fluctuation spectrum is that of 8 bosonic and 8 fermionic degrees of freedom with equal masses. We show that in the special case of the AdS2 x S2 superstring model the reduced theory is supersymmetric: it is equivalent to the (2,2) supersymmetric extension of the sine-Gordon model.
Posted by: IC
Wed
14 Nov 2007
Small, medium and giant magnons
Gordon Semenoff
(University of British Columbia)
Abstract:
The spin chain analogy of the problem of computing conformal dimensions of compostie operators in N=4 super Yang-Mills theory and the idea that the theory and its string dual could be integrable and could perhaps be solved by a Bethe ansatz has attracted a lot of attention. The present view is that this should be done in two steps. First one must solve the asymptotic Bethe ansatz which should obtain the spectrum of infinitely large operators where the problem simplifies considerably, being posed as scattering of magnons with a factorized S-matrix. Subsequently a thermodynamic Bethe ansatz should be used to find the spectrum of finite size operators. An interesting window onto finite size effects is the giant magnon, the string dual of the spin chain magnon. The seminar will discuss the giant magnon solution of string theory and attempts to interpret its finite size effects as the spectrum of a single magnon on an orbifolded version of N=4 Yang-Mills theory with reduced supersymmetry.
The spin chain analogy of the problem of computing conformal dimensions of compostie operators in N=4 super Yang-Mills theory and the idea that the theory and its string dual could be integrable and could perhaps be solved by a Bethe ansatz has attracted a lot of attention. The present view is that this should be done in two steps. First one must solve the asymptotic Bethe ansatz which should obtain the spectrum of infinitely large operators where the problem simplifies considerably, being posed as scattering of magnons with a factorized S-matrix. Subsequently a thermodynamic Bethe ansatz should be used to find the spectrum of finite size operators. An interesting window onto finite size effects is the giant magnon, the string dual of the spin chain magnon. The seminar will discuss the giant magnon solution of string theory and attempts to interpret its finite size effects as the spectrum of a single magnon on an orbifolded version of N=4 Yang-Mills theory with reduced supersymmetry.
Posted by: KCL
Wed
14 Nov 2007
Holographic Aspects of Generalized Electric-Magnetic Duality
Anastasios Petkou
(University of Crete)
Tue
13 Nov 2007
Hedgehog black holes and the deconfinement transition
Matthew Headrick
(Stanford)
Tue
13 Nov 2007
Models with a nontrivial metric in quantum mechanics
Miloslav Znojil
(Nuclear Physics Institute, Prague)
Abstract:
A not entirely formal discussion of some aspects of the so called PT-symmetric quantum mechanics will involve the following four more or less open problems:
1. What are chances of a closed-form description of boundaries of stability (i.e., of the allowed domain D of physical parameters) in a generic PT-symmetric model? (hint: we shall demonstrate that they are better than expected)
2. What happens if the coordinates are allowed to be topologically nontrivial? (hint: one gets the so called quantum toboggans)
3. Should and could a realistic PT-symmetric model be also based on a non-Hermitian form of the parity? (we intend to recommend it)
4. Could the use of a realistic PT-symmetric model be made compatible with a time-dependent metric? (we shall show how).
A not entirely formal discussion of some aspects of the so called PT-symmetric quantum mechanics will involve the following four more or less open problems:
1. What are chances of a closed-form description of boundaries of stability (i.e., of the allowed domain D of physical parameters) in a generic PT-symmetric model? (hint: we shall demonstrate that they are better than expected)
2. What happens if the coordinates are allowed to be topologically nontrivial? (hint: one gets the so called quantum toboggans)
3. Should and could a realistic PT-symmetric model be also based on a non-Hermitian form of the parity? (we intend to recommend it)
4. Could the use of a realistic PT-symmetric model be made compatible with a time-dependent metric? (we shall show how).
Posted by: KCL
Tue
13 Nov 2007
On the Riemann-Hilbert-Birkhoff inverse monodromy problem and the asymptotic analysis of the third Painleve transcendents
David Niles
(Dijon)
Mon
12 Nov 2007
Open/closed topological field theory and topological gravity
Ezra Getzler
Wed
7 Nov 2007
Berry's Phase, Supersymmetry and D-Branes
📍 London
David Tong
(DAMTP)
Abstract:
Berry's phase is a beautiful and simple idea in quantum mechanics, with application to many areas of condensed matter physics. After reviewing the non-Abelian version of Berry's phase, I will explain how this concept naturally fits together with supersymmetry. I will then show how to compute Berry's phase in D-brane systems, using both traditional quantum mechanics, as well as AdS/CFT techniques.
Berry's phase is a beautiful and simple idea in quantum mechanics, with application to many areas of condensed matter physics. After reviewing the non-Abelian version of Berry's phase, I will explain how this concept naturally fits together with supersymmetry. I will then show how to compute Berry's phase in D-brane systems, using both traditional quantum mechanics, as well as AdS/CFT techniques.
Posted by: KCL
Wed
7 Nov 2007
Strings on conifolds from strong coupling
David Berenstein
(University of California, Santa Barbara)
Abstract:
I will talk about a new method of performing a strong coupling expansion for many superconformal field theories in four dimensions, in particular those that are relavant for the AdS/CFT correspondence. I will first explain the methods for the case of N=4 SYM, as well as what calculations can be done (both analytically and numerically) and I will show how they compare with the dual AdS geometry. I will then explain what generalizations are required for other setups and what new field theory calculations can be done with these methods that were not available before.
I will talk about a new method of performing a strong coupling expansion for many superconformal field theories in four dimensions, in particular those that are relavant for the AdS/CFT correspondence. I will first explain the methods for the case of N=4 SYM, as well as what calculations can be done (both analytically and numerically) and I will show how they compare with the dual AdS geometry. I will then explain what generalizations are required for other setups and what new field theory calculations can be done with these methods that were not available before.
Posted by: IC
Tue
6 Nov 2007
Asymptotics of biorthogonal polynomials associated to the two-matrix model
Maurice Duits
(KU Leuven)
Abstract:
I will report on some joint work with Arno Kujlaars on the two-matrix model in random matrix theory. In this model one is interested in the eigenvalue statistics for two NxN hermitian Matrices, M1 and M2, taken random from exp(-NTrV(M1)-NTrW(M2)+tauTrM1M2)dM1dM2. Here V and W are two polynomials of even degree and tau is called coupling contant.
The eigenvalues statistics of M1 and M2 can be expressed in terms of certain biorthogonal polynomials. Therefore, if one can find asymptoticss for the biorthogonal polynomials then one also knowns the asymptotics for the eigenvalue statistics. Asymptotic results for the biorthogonal polynomials are known in the physics literature, however, they are without rigurous proofs. I will discuss a rigorous approach for a special case. The key element is a Deift-Zhou steepest descent analysis for a 4x4 Riemann-Hilbert problem.
I will report on some joint work with Arno Kujlaars on the two-matrix model in random matrix theory. In this model one is interested in the eigenvalue statistics for two NxN hermitian Matrices, M1 and M2, taken random from exp(-NTrV(M1)-NTrW(M2)+tauTrM1M2)dM1dM2. Here V and W are two polynomials of even degree and tau is called coupling contant.
The eigenvalues statistics of M1 and M2 can be expressed in terms of certain biorthogonal polynomials. Therefore, if one can find asymptoticss for the biorthogonal polynomials then one also knowns the asymptotics for the eigenvalue statistics. Asymptotic results for the biorthogonal polynomials are known in the physics literature, however, they are without rigurous proofs. I will discuss a rigorous approach for a special case. The key element is a Deift-Zhou steepest descent analysis for a 4x4 Riemann-Hilbert problem.
Posted by: brunel
Mon
5 Nov 2007
Open/closed topological field theory and topological gravity
Ezra Getzler
Thu
1 Nov 2007
Constructing One-Loop Amplitudes in QCD
Ruth Britto
(Amsterdam)
October 2007
Wed
31 Oct 2007
Closed strings and magnetised D-branes in toroidal compactifications
📍 London
Rodolfo Russo
(Queen Mary)
Abstract:
I will reconsider toroidal compactifications of bosonic string theory with particular regard to the phases (cocycles) necessary for a consistent definition of the vertex operators, the boundary states, and the T-duality rules. I will then use these ingredients to compute the
planar multi-loop partition function describing the interaction among magnetised or intersecting D-branes. Finally I will examine the degeneration limit of the 2-loop partition function and show that one obtains known and new tree-level 3-point correlators between twist fields.
I will reconsider toroidal compactifications of bosonic string theory with particular regard to the phases (cocycles) necessary for a consistent definition of the vertex operators, the boundary states, and the T-duality rules. I will then use these ingredients to compute the
planar multi-loop partition function describing the interaction among magnetised or intersecting D-branes. Finally I will examine the degeneration limit of the 2-loop partition function and show that one obtains known and new tree-level 3-point correlators between twist fields.
Posted by: KCL
Wed
31 Oct 2007
Highly Excited Mesons, Linear Regge Trajectories and the Pattern of the Chiral Symmetry Realization
Arkady Vainshtein
(University of Minnesota)
Abstract:
The chiral symmetry of QCD shows up in the linear Weyl–Wigner mode at short Euclidean distances or at high temperatures. On the other hand, low-lying hadronic states exhibit the nonlinear Nambu–Goldstone mode. An interesting question was raised as to whether the linear realization of the chiral symmetry is asymptotically restored for highly excited states. We address it in a number of ways. On the phenomenological side we argue that to the extent the meson Regge trajectories are observed to be linear and equidistant, the Weyl–Wigner mode is not realized. This picture is supported by quasiclassical arguments implying that the quark spin interactions in high excitations are weak, the trajectories are linear, and there is no chiral symmetry restoration. Then we use the string/gauge duality. In the top-down Sakai–Sugimoto construction the nonlinear realization of the chiral symmetry is built in. In the bottom-up AdS/QCD construction by Erlich et al., and Karch et al. the situation is more ambiguous. However, in this approach linearity and equidistance of the Regge trajectories can be naturally implemented, with the chiral symmetry in the Nambu–Goldstone mode. Asymptotic chiral symmetry restoration might be possible if a nonlinearity (convergence) of the Regge trajectories in an intermediate window of n,J, beyond the explored domain, takes place. This would signal the failure of the quasiclassical picture.
The chiral symmetry of QCD shows up in the linear Weyl–Wigner mode at short Euclidean distances or at high temperatures. On the other hand, low-lying hadronic states exhibit the nonlinear Nambu–Goldstone mode. An interesting question was raised as to whether the linear realization of the chiral symmetry is asymptotically restored for highly excited states. We address it in a number of ways. On the phenomenological side we argue that to the extent the meson Regge trajectories are observed to be linear and equidistant, the Weyl–Wigner mode is not realized. This picture is supported by quasiclassical arguments implying that the quark spin interactions in high excitations are weak, the trajectories are linear, and there is no chiral symmetry restoration. Then we use the string/gauge duality. In the top-down Sakai–Sugimoto construction the nonlinear realization of the chiral symmetry is built in. In the bottom-up AdS/QCD construction by Erlich et al., and Karch et al. the situation is more ambiguous. However, in this approach linearity and equidistance of the Regge trajectories can be naturally implemented, with the chiral symmetry in the Nambu–Goldstone mode. Asymptotic chiral symmetry restoration might be possible if a nonlinearity (convergence) of the Regge trajectories in an intermediate window of n,J, beyond the explored domain, takes place. This would signal the failure of the quasiclassical picture.
Posted by: IC
Thu
25 Oct 2007
Aspects of Gauge-Theory Orbit Space
Peter Orland
(New york)
Wed
24 Oct 2007
String vacua and algebraic geometry: an algorithmic approach
📍 London
Andre Lukas
(Oxford)
Wed
24 Oct 2007
Backreacting Flavors in the KS Background: a New Cascade
Francesco Benini
(SISSA)
Abstract:
I present new analytic solutions of type IIB supergravity with fully backreacting D7-branes describing the addition of an arbitrary number of flavors to the Klebanov-Tseytlin and Klebanov-Strassler theories. I provide a detailed analysis of the field theory and of the duality cascade which describes its RG flow, Seiberg duality is understood as a large gauge transformation in supergravity. Moreover the string background suggests that the UV behavior is a duality wall.
I present new analytic solutions of type IIB supergravity with fully backreacting D7-branes describing the addition of an arbitrary number of flavors to the Klebanov-Tseytlin and Klebanov-Strassler theories. I provide a detailed analysis of the field theory and of the duality cascade which describes its RG flow, Seiberg duality is understood as a large gauge transformation in supergravity. Moreover the string background suggests that the UV behavior is a duality wall.
Posted by: IC
Mon
22 Oct 2007
Open/closed topological field theory and topological gravity
Ezra Getzler
(Northwestern University)
Abstract:
The lectures will start by reviewing closed topological theories, before moving to more recent work in the open/closed theory on spaces with boundary.
From the work of Witten, the topology of the so-called Deligne-Mumford moduli spaces of Riemann surfaces with nodes plays a fundamental role in 2-dimensional topological gravity (known to mathematicians as Gromov-Witten theory). For example, by the work of Kontsevich and Manin, it is seen to underly the Witten-Dijkgraaf-Verlinde-Verlinde equation, and hence is intimately related to the theory of Frobenius manifolds and of integrable systems.
Most work on these moduli spaces has been focussed on the case of closed topological field theory. In these lectures, I will explore the moduli spaces, analogous to Deligne-Mumford moduli spaces, which play the corresponding role in the open theory. In this case, the world sheet (Riemann surface) has a boundary, and as a result, the moduli spaces are no longer complex orbifolds, but rather real orbifolds with corners. These moduli spaces may be viewed as an explanation of the way that algebraic structures, such as A-infinity categories, cyclic homology, and the Cardy condition, enter topological field theory in two dimensions. This theory should also have applications to understanding the foundations of string theory.
The lectures will start by reviewing closed topological theories, before moving to more recent work in the open/closed theory on spaces with boundary.
From the work of Witten, the topology of the so-called Deligne-Mumford moduli spaces of Riemann surfaces with nodes plays a fundamental role in 2-dimensional topological gravity (known to mathematicians as Gromov-Witten theory). For example, by the work of Kontsevich and Manin, it is seen to underly the Witten-Dijkgraaf-Verlinde-Verlinde equation, and hence is intimately related to the theory of Frobenius manifolds and of integrable systems.
Most work on these moduli spaces has been focussed on the case of closed topological field theory. In these lectures, I will explore the moduli spaces, analogous to Deligne-Mumford moduli spaces, which play the corresponding role in the open theory. In this case, the world sheet (Riemann surface) has a boundary, and as a result, the moduli spaces are no longer complex orbifolds, but rather real orbifolds with corners. These moduli spaces may be viewed as an explanation of the way that algebraic structures, such as A-infinity categories, cyclic homology, and the Cardy condition, enter topological field theory in two dimensions. This theory should also have applications to understanding the foundations of string theory.
Posted by: IC
Thu
18 Oct 2007
Scattering Amplitudes via AdS/CFT
Luis F. Alday
(Utrecht)
Wed
17 Oct 2007
Matrix Factorizations, D-branes and Homological Mirror Symmetry
📍 London
Wolfgang Lerche
(CERN)
Abstract:
We will review in simple terms how mirror symmetry works for general D-brane configurations, and in particular discuss how abstract mathematical concepts can be realized by physical LG models based on matrix factorizations. As for an application of these methods, we will explain how to explicitly compute exact, instanton-corrected effective superpotentials.
(Directions to the room can be found on the triangle website http://brahms.mth.kcl.ac.uk/cgi-bin/main.pl?action=triangle)
We will review in simple terms how mirror symmetry works for general D-brane configurations, and in particular discuss how abstract mathematical concepts can be realized by physical LG models based on matrix factorizations. As for an application of these methods, we will explain how to explicitly compute exact, instanton-corrected effective superpotentials.
(Directions to the room can be found on the triangle website http://brahms.mth.kcl.ac.uk/cgi-bin/main.pl?action=triangle)
Posted by: KCL
Wed
17 Oct 2007
Near-Integrability in 2+1-Dimensional Yang-Mills Theory
📍 London
Peter Orland
(City University of New York)
Abstract:
Pure Yang-Mills theory (with no matter) in 2+1-dimensions can be thought of as a system of 1+1 integrable field theories coupled together. These theories decouple in an anisotropic limit. This fact makes confinement and the mass gap simple to understand. This is the only analytic approach to this problem which does not rely on strong-coupling assumptions. Exact knowledge of the S-matrix and form factors of these integrable theories can be used to reveal details of the static potential between quarks and the mass spectrum. If a further assumption is made, the isotropic case should also be accessible to this technique.
Pure Yang-Mills theory (with no matter) in 2+1-dimensions can be thought of as a system of 1+1 integrable field theories coupled together. These theories decouple in an anisotropic limit. This fact makes confinement and the mass gap simple to understand. This is the only analytic approach to this problem which does not rely on strong-coupling assumptions. Exact knowledge of the S-matrix and form factors of these integrable theories can be used to reveal details of the static potential between quarks and the mass spectrum. If a further assumption is made, the isotropic case should also be accessible to this technique.
Posted by: KCL
Wed
10 Oct 2007
Towards lattice simulation of the gauge theory duals to black holes and hot strings
📍 London
Toby Wiseman
(Imperial College)
Wed
10 Oct 2007
Confinement in N=1 SQCD
Mikhail Shifman
(University of Minnesota)
Abstract:
We consider N=1 supersymmetric quantum chromodynamics (SQCD) with the gauge group U(Nc) and Nc+N quark flavors. Nc flavors are massless, the corresponding squark fields develop (small) vacuum expectation values (VEVs) on the Higgs branch. Extra N flavors are endowed with small (and equal) mass terms. We study this theory through its Seiberg's dual: U(N) gauge theory with Nc +N flavors of dual quark fields plus a gauge-singlet mesonic field M. The original theory is referred to as quark theory while the dual one is termed monopole theory. The suggested mild deformation of Seiberg's procedure changes the dynamical regime of the monopole theory from infrared free to asymptotically free at large distances. We show that, upon condensation of the dual quarks, the dual theory supports non-Abelian flux tubes (strings). Seiberg's duality is extended beyond purely massless states to include light states on both sides. Being interpreted in terms of the quark theory, the monopole-theory flux tubes are supposed to carry chromoelectric fields. The string junctions - confined monopole-theory monopoles - can be viewed as constituent quarks of the original quark theory. We interpret closed strings as glueballs of the original quark theory. Moreover, there are string configurations formed by two junctions connected by a pair of different non-Abelian strings. These can be considered as constituent quark mesons of the quark theory.
We consider N=1 supersymmetric quantum chromodynamics (SQCD) with the gauge group U(Nc) and Nc+N quark flavors. Nc flavors are massless, the corresponding squark fields develop (small) vacuum expectation values (VEVs) on the Higgs branch. Extra N flavors are endowed with small (and equal) mass terms. We study this theory through its Seiberg's dual: U(N) gauge theory with Nc +N flavors of dual quark fields plus a gauge-singlet mesonic field M. The original theory is referred to as quark theory while the dual one is termed monopole theory. The suggested mild deformation of Seiberg's procedure changes the dynamical regime of the monopole theory from infrared free to asymptotically free at large distances. We show that, upon condensation of the dual quarks, the dual theory supports non-Abelian flux tubes (strings). Seiberg's duality is extended beyond purely massless states to include light states on both sides. Being interpreted in terms of the quark theory, the monopole-theory flux tubes are supposed to carry chromoelectric fields. The string junctions - confined monopole-theory monopoles - can be viewed as constituent quarks of the original quark theory. We interpret closed strings as glueballs of the original quark theory. Moreover, there are string configurations formed by two junctions connected by a pair of different non-Abelian strings. These can be considered as constituent quark mesons of the quark theory.
Posted by: IC
Wed
3 Oct 2007
Exploring 5-dimensional holographic duals to QCD
📍 London
Francesco Nitti
(Ecole Polytechnique)
Wed
3 Oct 2007
Nonabelian strings in the gauge theories
Alexander Gorsky
(ITEP)
Abstract:
We will discuss the nonabelian strings found recently in SUSY QCD and non-SUSY gauge theories with scalars. Their properties will be considered in some details. In particular, their rich worldsheet structure involving localized monopoles will be explained. The dependence on the SUSY breaking parameters will be analysed.
We will discuss the nonabelian strings found recently in SUSY QCD and non-SUSY gauge theories with scalars. Their properties will be considered in some details. In particular, their rich worldsheet structure involving localized monopoles will be explained. The dependence on the SUSY breaking parameters will be analysed.
Posted by: IC
September 2007
Thu
27 Sep 2007
Exploring holographic theories for QCD
Umut Gursoy
(Polytechnique and ENS, Paris)