Integrability in Sigma-Models

Abstract

This is a write-up of lectures on integrable sigma-models, which covers the following topics: (1) Homogeneous spaces, (2) Classical integrability of sigma-models in two dimensions, (3) Topological terms, (4) Background-field method and beta-function, (5) S-matrix bootstrap in the O(N) model, (6) Supersymmetric cosets and strings on AdS(d)xX.

46 pages, 12 figures, based on lectures at the Les Houches summer school "Integrability: From Statistical Systems To Gauge Theory" (Les Houches, 6.06-1.07. 2016)

References in corpus (5)

• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Type IIB superstring action in AdS_5 x S^5 background
• How Algebraic Bethe Ansatz works for integrable model
• Strings on Semisymmetric Superspaces
• Quantum Giant Magnons

Cited by in corpus (7)

• Gauge Theory and Integrability, II
• Integrable Deformations of Sigma Models
• Non-integrability on AdS${}_3$ supergravity backgrounds
• Flag manifold sigma models: spin chains and integrable theories
• Sigma models as Gross-Neveu models
• Flag manifold sigma-models: the 1/N-expansion and the anomaly two-form
• Integrability treatment of AdS/CFT orbifolds