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We introduce a class of 2D sigma models which are parametrized by a function of one variable. In addition to the physical field g, these models include an auxiliary field vα which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor. Published by the American Physical Society 2024
Ferko et al. (Thu,) studied this question.