# Integrable Coupled $\sigma$ Models

Delduc, F. (Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France) ; Lacroix, S. (Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany and Zentrum für Mathematische Physik, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany) ; Magro, M. (Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France) ; Vicedo, B. (Department of Mathematics, University of York, York YO10 5DD, United Kingdom)

28 January 2019

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.

Published in: Physical Review Letters 122 (2019)