Integrable Higher-Spin Deformations of Sigma Models from Auxiliary Fields

TL;DR

This paper introduces a new class of integrable deformations of the principal chiral model involving higher-spin currents, demonstrating their Lax representation, Poisson structure, and compatibility with T-duality and Wess-Zumino terms.

Contribution

It constructs an infinite family of integrable sigma model deformations using auxiliary fields, extending previous formalisms to include higher-spin currents and Wess-Zumino terms.

Findings

Models admit Lax representation and Maillet Poisson brackets

Non-Abelian T-duals are classically integrable

Deformations are compatible with Wess-Zumino terms

Abstract

We construct a new infinite family of integrable deformations of the principal chiral model (PCM) parameterized by an interaction function of several variables, which extends the formalism of arXiv:2405.05899, and includes deformations of the PCM by functions of both the stress tensor and higher-spin conserved currents. We show in detail that every model in this class admits a Lax representation for its equations of motion, and that the Poisson bracket of the Lax connection takes the Maillet form, establishing the existence of an infinite set of Poisson-commuting conserved charges. We argue that the non-Abelian T-dual of any model in this family is classically integrable, and that T-duality "commutes" with a general deformation in this class, in a sense which we make precise. Finally, we demonstrate that these higher-spin auxiliary field deformations can be extended to accommodate the addition of a Wess-Zumino term, and we exhibit the Lax connection in this case.