Conference on Integrability in Gauge and String Theory 2010

28 Jun 2010, 08:00 → 2 Jul 2010, 18:00 Europe/Stockholm

Oskar Klein lecture hall (Nordita)

Giuseppe Policastro (ENS Paris), Joseph Minahan (Uppsala University), Konstantin Zarembo (ENS Paris), Lisa Freyhult (Uppsala University), Shiraz Minwalla (Tata Institute, Mumbai)

The use of integrability has lead to remarkable progress in our understanding of non-perturbative dynamics in gauge theories and their relationship to string theory. Highly unexpected links between supersymmetric field theory, spin chains, and two-dimensional sigma-models have been discovered in recent years. These developments have lead to exact solutions for the dimensions of operators in planar N=4 supersymmetric Yang-Mills theory in four dimensions to any loop order. This is the first case where exact results of this type have been found for any interacting four dimensional field theory.

Progress in this field has been continuing at a rapid pace. This includes: applying the thermodynamic Bethe ansatz (TBA) and the development of the Y-system to compute so called finite size effects for operators with small engineering dimensions; computing scattering amplitudes at strong coupling using the integrability of the string world-sheet; finding new results in superconformal Chern-Simons theory.

The IGST2010 conference is intended to bring together experts in gauge theories, strings, and integrable systems in order to create a discussion forum for future developments in this rapidly evolving field. The conference will consist of 25 talks, each 50 minutes in length and with time allowed for questions afterward. Invitations for many of the speaking slots will be made later to allow for the latest developments.

The last day to register for the conference is 15 May 2010. The conference is part of the program "Integrability in String and Gauge Theories; AdS/CFT Duality and its Applications" which runs from 31 May to 09 July 2010 at Nordita. Please note that the conference registration is different than the registration for the program.

Information about the boat trip vaxholm_-_ss_stockholm.pdf

Where to have lunch? nordita_restaurants_small.png

Monday 28 June

09:00 Registration

1 Welcome

Speaker: Lárus Thorlacius (Nordita)

2 Integrability of high energy scattering amplitudes in N=4 SUSY

Speaker: Lev Lipatov (Petersburg Nuclear Physics Institute)

Slides Lipatov.pdf

11:00 break

3 Quantum integrable spin systems and generalized Schur - Weyl duality

There are integrable (solvable) spin systems related to quantum groups (quasi-triangular Hopf algebras), with simple structure of space of states. The integrals of motion belong to a quotient A of the braid group, which is a centralizer of the symmetry quantum group of the system. The space of states is a direct sum of of tensor products of corresponding irreducible representations of A and the quantum group. This decomposition is multiplicity free.

Speaker: Petr Kulish (St. Petersburg Department of Steklov Mathematical Institute)

Slides Kulish_partII.pdf kulish-transparency.pdf

12:30 lunch

4 One-point functions for sine-Gordon model at finite temperature.

We apply the hidden fermionic structure of integrable models for computing the one-point functions of the primary fields and their descendants for Eucildean sine-Gordon model on the cylinder (at finite temperature). This allows in principle to write down the complete asymptotic series for the two-point functions.

Speaker: Fedor Smirnov (LPTHE, Paris)

Slides Smirnov.pdf

5 Non-planarity and Integrability

Speaker: Charlotte Kristjansen (Niels Bohr Institutet, Copenhagen)

Slides Kristjansen.pdf

16:30 break

6 Q-Operator Demystified

I will present a novel construction of the Q-operator for systems with sl(n|m) symmetry.

Speaker: Matthias Staudacher (Humboldt Universität zu Berlin)

Slides staudacher.pdf

18:30 Reception

Tuesday 29 June

7 The worldsheet low-energy limit of the AdS_4 x CP^3 superstring

Speaker: Dmitry BYKOV

Slides Bykov.pdf

11:00 break

8 Why Y? Exploiting Hirota integrable dynamics in AdS/CFT

Speaker: Vladimir KAZAKOV

Slides Kazakov.pptx

12:30 lunch

9 TBA and functional relations for the AdS_5/CFT_4 correspondence

The exact anomalous dimensions of the single trace composite operators in the planar limit of $N=4$ super Yang-Mills can be studied in the framework of the Thermodynamic Bethe Ansatz method (TBA). In this talk, I will discuss the analytic properties of the TBA solutions -the Y-functions- and the associated set of functional relations -the Y-system-. Contrary to the more studied relativistic invariant cases, the $AdS_5/CFT_4$-related Y-functions live on multi-sheeted coverings of the complex plane with an infinite number of square-root branch points. As a direct consequence of this fact, the TBA equations and in particular the dressing kernel cannot be obtained from the Y-system without extra information on the square-root discontinuities across semi-infinite segments in the complex plane. It is shown that the discontinuity functions fulfill an independent simple set of local functional equations. The Y-system extended by the discontinuity relations forms a fundamental set of local non-linear constraints that can be easily transformed into integral form through Cauchy's theorem.

Speaker: Roberto Tateo (universita` di Torino)

Slides Tateo.pdf

10 On the Mirror TBA

I will discuss some subtleties of the Thermodynamic Bethe Ansatz for the AdS_5 x S^5 mirror model concerning the construction of excited states and their analytic properties. I will then use the TBA equations to derive the five-loop anomalous dimension of the Konishi operator and argue that the corresponding result agrees with the one obtained via the generalized Luscher formulae.

Speaker: Gleb Arutyunov (Universiteit Utrecht)

Slides Arutyunov.pdf

16:30 break

11 The classical R-matrix of AdS/CFT

After reviewing the R-matrix approach to classical integrable systems, we formulate the classical integrable structure of sigma-models relevant to the AdS/CFT correspondence.

Speaker: Benoit Vicedo (Saclay)

Slides Vicedo.pdf

Wednesday 30 June

12 Quantum Deformations of Worldsheet Scattering

Speaker: Niklas Beisert (AEI, Potsdam)

Slides Beisert.pdf

11:00 break

13 Spin Chains for N=2 Superconformal Theories: Integrability in the Veneziano Limit?

Speaker: Leonardo Rastelli (Stony Brook University)

Slides Rastelli.pdf

12:30 lunch

14 An operator product expansion for null polygonal Wilson loops

We consider polygonal Wilson loops with null edges in conformal gauge theories. We derive an OPE-like expansion when several successive lines of the polygon are becoming aligned. The limit corresponds to a collinear, or multicollinear, limit and we explain the systematics of all the subleading corrections, going beyond the leading terms that were previously considered. These subleading corrections are governed by excitations of high spin operators, or excitations of a flux tube that goes between two Wilson lines. The discussion is valid for any conformal gauge theory, for any coupling and in any dimension. For N=4 super Yang Mills we check this expansion at strong coupling and at two loops at weak coupling . We also make predictions for the remainder function at higher loops. We will also discuss aspects of the excitations around the relevant flux tube or "sea of derivatives''

Speaker: Juan Maldacena (IAS Princeton)

Slides Maldacena.pdf

15 A & B model approaches to surface operators and Toda theories

In the first part I will give an overview of the recent results relating 4d N=2 quiver gauge theories, 2d conformal Toda field theories, topological string theories and quiver matrix models. In the second part surface operators in the gauge theories and their dual interpretations in the other classes of theories will be discussed

Speaker: Niclas Wyllard

Slides Wyllard.pdf

16:30 break

16 Yangians and Grassmannians in N=4 super Yang-Mills

Speaker: Livia Ferro (LAPTH Annecy)

Slides Ferro.pdf

Thursday 1 July

17 Perturbative quantum gravity from gauge theory

In recent years it has become clear that gauge theory and gravity amplitudes exhibit remarkable simplicity and beautiful structures. Here I will discuss one such structure: a duality between color and kinematics in gauge theory amplitudes. The duality implies nontrivial relations between color-ordered partial tree amplitudes. Remarkably the duality dictates the construction of gravity amplitudes as a double copy of gauge theory kinematic factors, clarifying the Kawai-Lewellen-Tye relations of open and closed strings. Originally considered as a classical (tree-level) duality, here I will present evidence that the duality is valid at the quantum level as well.

Speaker: Henrik Johansson (Saclay)

Slides Johansson.pdf

11:00 break

18 Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills

Speaker: Johannes Henn (Humboldt Universität zu Berlin)

Slides Henn.pdf

12:30 lunch

19 Classical Polylogarithms for Amplitudes and Wilson Loops

Speaker: Marcus Spradlin (Brown University)

Slides spradlin2.pdf

20 The Y-system for scattering amplitudes

We compute N=4 Super Yang Mills planar amplitudes at strong coupling by considering minimal surfaces in AdS_5 space. The surfaces end on a null polygonal contour at the boundary of AdS. We show how to compute the area of the surfaces as a function of the conformal cross ratios characterizing the polygon at the boundary. These equations have the form of Thermodynamic Bethe Ansatz equations. The area is the free energy of the TBA system. We consider any number of gluons and in any kinematic configuration.

Speaker: Pedro Vieira (Perimeter Institute)

16:30 break

21 Superconformal invariance of scattering amplitudes in N=4 super-Yang-Mills theory

We discuss the realization of dual and conventional superconformal symmetries on the scattering amplitudes in N=4 SYM. While these symmetries are exact at tree level, they have to be complemented with analytic properties to fully fix the tree. At loop level both symmetries are broken by different mechanisms. We describe the formulation of amplitudes in twistor space and in terms of Grassmannian invariants.

Speaker: Emery Sokatchev (LAPTH, Annecy)

Slides Sokatchev.pdf

18:00 dinner

Friday 2 July

22 5-loop test of the AdS/CFT spectral equations

I will review the computation of the anomalous dimension for twist-2 operators at five loop order at weak coupling. This result provides us with data for testing the veracity of the spectral equations for planar AdS/CFT.

Speaker: Tomasz Łukowski (Uniwersytet Jagielloński, Kraków)

Slides Lukowski.pdf

23 Weak coupling tests of the mirror TBA

The mirror Thermodynamic Bethe Ansatz (TBA) approach offers a tool to investigate the spectrum of AdS/CFT in the planar limit. The TBA equations governing the spectrum are based on several conjectures this is why it is important to test them carefully. In this talk we will focus on the analytical tests of the AdS/CFT TBA system in the weak coupling limit and show that the 5-loop anomalous dimensions of the twist-2 operators of the sl(2) sector derived from the TBA equations agree with the results obtained previously from the generalized Luscher formulae.

Speaker: Arpad Hegedus (KFKI, Budapest)

Slides Hegedus.pdf

11:30 break

24 Correlation functions of operators dual to classical string states

Speaker: Romuald Janik (Uniwersytet Jagielloński, Kraków)

Slides Janik.pdf

13:00 lunch

25 Strings in the AdS light-cone gauge and the generalized scaling function

Speaker: Radu Roiban (Pennsylvania State University)

Slides Roiban.pdf

26 Summary talk

Speaker: Arkady Tseytlin (Imperial College London)

Slides Tseytlin.pdf