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arXiv · 2405.05899

Infinite Family of Integrable Sigma Models Using Auxiliary Fields

Christian Ferko·Liam Smith
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Abstract

We introduce a class of $2d$ sigma models which are parameterized by a function of one variable. In addition to the physical field $g$, these models include an auxiliary field $v_\alpha$ 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.

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Christian Ferko, Liam Smith. 2024-05-09. Infinite Family of Integrable Sigma Models Using Auxiliary Fields. https://doi.org/10.1103/physrevlett.133.131602

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