SCIENTIFIC DIRECTION : P. Dorey (Durham U.), G. Korchemsky (IPhT Saclay), N. Nekrasov (SCGP Stony Brook/IHES Bures sur Yvette), V. Schomerus , (DESY), D. Serban (IPhT Saclay)

Over the few previous decades, integrability has become a tool of choice in studying classical and quantum interacting systems, being one of the few non-perturbative methods at hand. For a long time it was restricted to one dimensional systems, or two space-time dimensions, and as such it found applications in low-dimensional systems in condensed matter physics. Integrability is deeply connected with exactly solvable statistical models, with two-dimensional conformal field theory, matrix models or with various fields in mathematics. In the last fifteen years, integrability found surprising applications in an entirely new approach to quantum gauge theories. New ideas arose from dualities between gauge and string theory. Through the spectacular and widely recognized successes in the calculation of anomalous dimensions and scattering amplitudes in planar N=4 super-Yang-Mills theory on the one hand, and the exact determination of the low-energy physics of N=2 super-Yang-Mills theories on the other hand, a completely new perspective on gauge theory is emerging: gauge theory as an integrable system. Moreover, a non-trivial relation between gauge theories with different amounts of supersymmetry seems to emerge, offering possibly tools for the analysis of non-supersymmetric gauge theory, such as QCD using the exact results from the supersymmetric world. The first non-trivial examples of quantum field theoretic calculations interpolating between the weak and the strong coupling are found.

The purpose of this school is to bring together young researchers with specialists from statistical physics, condensed matter physics, gauge and string theory and mathematics. We would like to provide the first with the necessary background for working in these rapidly evolving research fields, and to stimulate cross-fertilization of the different research areas.