Integrability : from statistical systems to gauge theory : lecture notes of the Les Houches Summer School. Volume 106, June 2016

This volume, 106 of the Les Houches Summer School series, brings together applications of integrability to supersymmetric gauge and string theory. The book focuses on the application of integrability and problems in quantum field theory. Particular emphasis is given to the exact solution of planar N=4 super-Yang-Mills theory and its relation with string theory on the one hand, and the exact determination of the low-energy physics of N=2 super-Yang-Mills theories on the other; links with other domains are also explored. The purpose of the Les Houches Summer School was to bring together young researchers and specialists from statistical physics, condensed matter physics, gauge and string theory, and mathematics, to stimulate discussion across these different research areas. 1: Jesper Lykke Jacobsen: Integrability in statistical systems and quantum spin chains2: Joerg Teschner: A guide to two-dimensional conformal field theory3: Gordon W. Semenoff: Lectures on the holographic duality of gauge fields and strings4: David Kosower: Introduction to Scattering Amplitudes5: Konstantin Zarembo: Integrability in Sigma-Models6: Sergei L. Lukyanov and Alexander B. Zamolodchikov: Integrability in 2D fields theory/sigma models7: Fabian H. L. Essler: Applications of Integrable Models in Condensed Matter and Cold Atom Physics8: Marius de Leeuw, Asger C. Ipsen, Charlotte Kristjansen, and Matthias Wilhelm: Introduction to Integrability and One-point Functions in N = 4 SYM and its Defect Cousin9: Nikolay Gromov: Spectrum of N=4 SYM and the Quantum Spectral Curve10: Shota Komatsu: Three-point Functions in N = 4 Supersymmetric Yang-Mills Theory11: Vesily Pestun: Localization and N=2 supersymmetric field theory This volume contains lectures delivered at the Les Houches Summer School 'Integrability: from statistical systems to gauge theory' held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics This volume brings together applications of integrability to supersymmetric gauge and string theory. It focuses on the application of integrability and problems in quantum field theory. Particular emphasis is given to the exact solution of planar N=4 super-Yang-Mills theory and its relation with string theory on the one hand, and the exact determination of the low-energy physics of N=2 super-Yang-Mills theories on the other; links with other domains are also explored Volume 106 in the Les Houches Summer School series brings together applications of integrability to supersymmetric gauge and string theory.