The classical Yangian symmetry of Auxiliary Field Sigma Models

TL;DR

This paper develops a systematic framework to understand the Yangian symmetry in integrable sigma models and their deformations, demonstrating the persistence of these symmetries across various models.

Contribution

It generalizes the BIZZ recursive procedure and provides conditions for Yangian algebra in deformed sigma models, unifying their integrability properties.

Findings

Yangian algebra and Maillet bracket structure found in all studied models

Unified explanation for the persistence of integrability under deformations

Generalized recursive procedure for non-local charge generation

Abstract

Integrable field theories exhibit infinitely many symmetries which underlie their solvability, but the structure of these symmetries can become obscured after performing an integrable deformation such as $\TT$ or an auxiliary field deformation. In this paper, we present a systematic organizing principle for understanding deformed charges and their Yangian structure in a broad class of integrable sigma models and their auxiliary field deformations. We generalize the recursive procedure of Brezin, Itzykson, Zinn-Justin, and Zuber (BIZZ) for generating non-local charges, and give sufficient conditions under which the resulting charges obey a Yangian algebra. We apply these results to many examples of integrable sigma models and their auxiliary field deformations, finding a Yangian algebra and Maillet bracket structure in all cases. This offers a unified explanation for the persistence of Hamiltonian integrability and Yangian symmetry across a wide landscape of deformed sigma models.