# Conference on Integrability in Gauge and String Theory 2010

Europe/Stockholm
Oskar Klein lecture hall (Nordita)

### Oskar Klein lecture hall

#### Nordita

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Description

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.

• Monday, June 28
• 9:00 AM
Registration Main entrance

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#### Nordita

• 1
Welcome Oskar Klein lecture hall

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Speaker: Lárus Thorlacius (Nordita)
• 2
Integrability of high energy scattering amplitudes in N=4 SUSY Oskar Klein lecture hall

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Speaker: Lev Lipatov (Petersburg Nuclear Physics Institute)
• 11:00 AM
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• 3
Quantum integrable spin systems and generalized Schur - Weyl duality Oskar Klein lecture hall

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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)
• 12:30 PM
lunch - (-)

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• 4
One-point functions for sine-Gordon model at finite temperature. Oskar Klein lecture hall

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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)
• 5
Non-planarity and Integrability Oskar Klein lecture hall

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Speaker: Charlotte Kristjansen (Niels Bohr Institutet, Copenhagen)
• 4:30 PM
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• 6
Q-Operator Demystified Oskar Klein lecture hall

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I will present a novel construction of the Q-operator for systems with sl(n|m) symmetry.
Speaker: Matthias Staudacher (Humboldt Universität zu Berlin)
• 6:30 PM
Reception Canteen

### Canteen

#### Nordita

• Tuesday, June 29
• 7
The worldsheet low-energy limit of the AdS_4 x CP^3 superstring Oskar Klein lecture hall

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Speaker: Dmitry BYKOV
• 11:00 AM
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• 8
Why Y? Exploiting Hirota integrable dynamics in AdS/CFT Oskar Klein lecture hall

• 12:30 PM
lunch -

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• 9
TBA and functional relations for the AdS_5/CFT_4 correspondence Oskar Klein lecture hall

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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)
• 10
On the Mirror TBA Oskar Klein lecture hall

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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)
• 4:30 PM
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• 11
The classical R-matrix of AdS/CFT Oskar Klein lecture hall

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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)
• Wednesday, June 30
• 12
Quantum Deformations of Worldsheet Scattering Oskar Klein lecture hall

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Speaker: Niklas Beisert (AEI, Potsdam)
• 11:00 AM
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• 13
Spin Chains for N=2 Superconformal Theories: Integrability in the Veneziano Limit? Oskar Klein lecture hall

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Speaker: Leonardo Rastelli (Stony Brook University)
• 12:30 PM
lunch -

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• 14
An operator product expansion for null polygonal Wilson loops Oskar Klein lecture hall

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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)
• 15
A & B model approaches to surface operators and Toda theories Oskar Klein lecture hall

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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
• 4:30 PM
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• 16
Yangians and Grassmannians in N=4 super Yang-Mills Oskar Klein lecture hall

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Speaker: Livia Ferro (LAPTH Annecy)
• Thursday, July 1
• 17
Perturbative quantum gravity from gauge theory Oskar Klein lecture hall

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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)
• 11:00 AM
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• 18
Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills Oskar Klein lecture hall

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Speaker: Johannes Henn (Humboldt Universität zu Berlin)
• 12:30 PM
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• 19
Classical Polylogarithms for Amplitudes and Wilson Loops Oskar Klein lecture hall

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• 20
The Y-system for scattering amplitudes Oskar Klein lecture hall

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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)
• 4:30 PM
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• 21
Superconformal invariance of scattering amplitudes in N=4 super-Yang-Mills theory Oskar Klein lecture hall

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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)
• 6:00 PM
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• Friday, July 2
• 22
5-loop test of the AdS/CFT spectral equations Oskar Klein lecture hall

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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)
• 23
Weak coupling tests of the mirror TBA Oskar Klein lecture hall

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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.
• 11:30 AM
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• 24
Correlation functions of operators dual to classical string states Oskar Klein lecture hall

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Speaker: Romuald Janik (Uniwersytet Jagielloński, Kraków)
• 1:00 PM
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• 25
Strings in the AdS light-cone gauge and the generalized scaling function Oskar Klein lecture hall

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Speaker: Radu Roiban (Pennsylvania State University)
• 26
Summary talk Oskar Klein lecture hall

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Speaker: Arkady Tseytlin (Imperial College London)