"Conference on Integrability in Gauge and String Theory 2010" chaired by
Shiraz Minwalla (Tata Institute, Mumbai)
, Lisa Freyhult (Uppsala University)
, Joseph Minahan (Uppsala University)
, Konstantin Zarembo (ENS Paris)
, Giuseppe Policastro (ENS Paris)

from Monday 28 June 2010
(08:00)
to Friday 02 July 2010
(18:00)
at
Nordita
(
Oskar Klein lecture hall
)

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.

Integrability of high energy scattering amplitudes in N=4 SUSY (1h00')
( Slides )

Lev Lipatov (Petersburg Nuclear Physics Institute)

11:00

break

11:30

Quantum integrable spin systems and generalized Schur - Weyl duality (1h00')
( Slides )

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

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.

12:30

lunch

14:30

One-point functions for sine-Gordon model at finite temperature. (1h00')
( Slides )

Fedor Smirnov (LPTHE, Paris)

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.

15:30

Non-planarity and Integrability (1h00')
( Slides )

Charlotte Kristjansen (Niels Bohr Institutet, Copenhagen)

TBA and functional relations for the AdS_5/CFT_4 correspondence (1h00')
( Slides )

Roberto Tateo (universita` di Torino)

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.

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.

16:30

break

17:00

The classical R-matrix of AdS/CFT (1h00')
( Slides )

Benoit Vicedo (Saclay)

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.

Quantum Deformations of Worldsheet Scattering (1h00')
( Slides )

Niklas Beisert (AEI, Potsdam)

11:00

break

11:30

Spin Chains for N=2 Superconformal Theories: Integrability in the Veneziano Limit? (1h00')
( Slides )

Leonardo Rastelli (Stony Brook University)

12:30

lunch

14:30

An operator product expansion for null polygonal Wilson loops (1h00')
( Slides )

Juan Maldacena (IAS Princeton)

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''

15:30

A & B model approaches to surface operators and Toda theories (1h00')
( Slides )

Niclas Wyllard

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

16:30

break

17:00

Yangians and Grassmannians in N=4 super Yang-Mills (1h00')
( Slides )

Perturbative quantum gravity from gauge theory (1h00')
( Slides )

Henrik Johansson (Saclay)

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.

11:00

break

11:30

Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills (1h00')
( Slides )

Johannes Henn (Humboldt Universität zu Berlin)

12:30

lunch

14:30

Classical Polylogarithms for Amplitudes and Wilson Loops (1h00')
( Slides )

Marcus Spradlin (Brown University)

15:30

The Y-system for scattering amplitudes (1h00')

Pedro Vieira (Perimeter Institute)

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.

16:30

break

17:00

Superconformal invariance of scattering amplitudes in N=4 super-Yang-Mills theory (1h00')
( Slides )

Emery Sokatchev (LAPTH, Annecy)

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.

5-loop test of the AdS/CFT spectral equations (1h00')
( Slides )

Tomasz Łukowski (Uniwersytet Jagielloński, Kraków)

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.

10:30

Weak coupling tests of the mirror TBA (1h00')
( Slides )

Arpad Hegedus (KFKI, Budapest)

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

break

12:00

Correlation functions of operators dual to classical string states (1h00')
( Slides )

Romuald Janik (Uniwersytet Jagielloński, Kraków)

13:00

lunch

14:15

Strings in the AdS light-cone gauge and the generalized scaling function (1h00')
( Slides )