## Integrability in QFT and AdS/CFT – HS 2013

**Lecturer:** Niklas Beisert

Thursdays 30.10., 14.10., 12.12., 19.12.

14:15-18:00, EPF Lausanne, BC 04

### Description

Integrable structures have played a very important role in obtaining exact results in interacting field theories and statistical systems, and they have had an important impact in our understanding of Quantum Field Theory and Statistical Mechanics. Many of the classical results in integrability concern two-dimensional systems, but recently it has been shown that many interacting quantum field theories in higher dimensions also have hidden integrable structures, most notably N=4 super Yang-Mills theory in the planar limit. This has led to a recent, enormous activity in the field, and many new exact results have been found which have played a crucial role in the development of the AdS/CFT correspondence. The aim of this course is to provide a pedagogical, graduate level introduction to integrability in Quantum Field Theory covering as well these recent developments. The course will start with a review of integrability in Quantum Field Theory in two dimensions (Bethe ansatz, thermodynamic Bethe ansatz), and then it will cover various aspects of integrability in N=4 super Yang-Mills theory.

#### Content

- Classical Integrability
- Classical Field Theory
- Integrable Spin Chains
- Quantum Integrability
- Statistical Mechanics
- Quantum Algebra
- AdS/CFT Integrability

#### Literature

- G. Arutyunov, "Students Seminar: Classical and Quantum Integrable Systems".
- O. Babelon, D. Bernard, M. Talon, "Introduction to Classical Integrable Systems", Cambridge University Press (2003).
- N. Beisert, "The Dilatation Operator of N = 4 super Yang-Mills Theory and Integrability", Phys. Rept. 405, 1-202 (2004), hep-th/0407277.
- N. Reshetikhin, "Lectures on the integrability of the 6-vertex model", arxiv:1010.5031.
- L.D. Faddeev, "How Algebraic Bethe Ansatz works for integrable model", hep-th/9605187.
- P. Zinn-Justin, "Six-Vertex, Loop and Tiling Models: Integrability and Combinatorics".
- D. Bernard, "An Introduction to Yangian Symmetries", Int. J. Mod. Phys. B7, 3517-3530 (1993), hep-th/9211133.
- V. Chari, A. Pressley, "A Guide to Quantum Groups", Cambridge University Press (1995).
- N. Beisert et al., "Review of AdS/CFT Integrability: An Overview", arxiv:1012.3982.

### Materials

#### Lecture Notes