Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities

Abstract

In the following paper, which is based on the authors PhD thesis submitted to Imperial College London, we explore the applicability of Yangian symmetry to various integrable models, in particular, in relation with S-matrices. One of the main themes in this work is that, after a careful study of the mathematics of the symmetry algebras one finds that in an integrable model, one can directly reconstruct S-matrices just from the algebra. It has been known for a long time that S-matrices in integrable models are fixed by symmetry. However, Lie algebra symmetry, the Yang-Baxter equation, crossing and unitarity, which are what constrains the S-matrix in integrable models, are often taken to be separate, independent properties of the S-matrix. Here, we construct scattering matrices purely from the Yangian, showing that the Yangian is the right algebraic object to unify all required symmetries of many integrable models. In particular, we reconstruct the S-matrix of the principal chiral field, and, up to a CDD factor, of other integrable field theories with su(n) symmetry. Furthermore, we study the AdS/CFT correspondence, which is also believed to be integrable in the planar limit. We reconstruct the S-matrices at weak and at strong coupling from the Yangian or its classical limit. We give a pedagogical introduction into the subject, presenting a unified perspective of Yangians and their applications in physics. This paper should hence be accessible to mathematicians who would like to explore the application of algebraic objects to physics as well as to physicists interested in a deeper understanding of the mathematical origin of physical quantities.

133 pages, accepted for publication in Reviews in Mathematical Physics

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Cited by in corpus (10)

• Lectures on Yangian Symmetry
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Lectures on S-matrices and Integrability
• The RTT-Realization for the Deformed gl(2|2) Yangian
• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
• Yangian Algebra and Correlation Functions in Planar Gauge Theories
• Nonlocal Symmetries and Factorized Scattering
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Multi-parametric R-matrix for the sl(2|1) Yangian