Integrable Coupled σ Models.

F Delduc,M Magro,S Lacroix,B Vicedo

doi:10.1103/physrevlett.122.041601

Abstract

A systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined. It is based on the recent interpretation of integrable field theories as realizations of affine Gaudin models. In this language, one can associate integrable field theories with affine Gaudin models having arbitrarily many sites. We present the result of applying this general procedure to couple together an arbitrary number of principal chiral model fields on the same Lie group, each with a Wess-Zumino term.

Highlights

Introduction.—The very scarceness of the property of integrability in classical and quantum systems makes its ubiquity in high energy physics as well as its rich history in condensed matter physics seem even more remarkable
A systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined. It is based on the recent interpretation of integrable field theories as realizations of affine Gaudin models
We present the result of applying this general procedure to couple together an arbitrary number of principal chiral model fields on the same Lie group, each with a Wess-Zumino term

Summary

Integrable Coupled σ Models

A systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined It is based on the recent interpretation of integrable field theories as realizations of affine Gaudin models. Classical integrable field theories which are known [16] to be realizations of this class of affine Gaudin models include the principal chiral model and integrable σ models obtained from it by adding a Wess-Zumino (WZ) term or by performing a non-Abelian T duality [18]. This class contains the inhomogeneous Yang-Baxter deformation with a Wess-Zumino term constructed in [22,11]

Published by the American Physical Society

Making use of the identity

Lax matrix