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arXiv · 2605.18213

The classical Yangian symmetry of Auxiliary Field Sigma Models

Daniele Bielli·Christian Ferko·Michele Galli·Gabriele Tartaglino-Mazzucchelli
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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.

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Daniele Bielli, Christian Ferko, Michele Galli, Gabriele Tartaglino-Mazzucchelli. 2026-05-18. The classical Yangian symmetry of Auxiliary Field Sigma Models. https://arxiv.org/abs/2605.18213

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