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arXiv · 2504.17294

Higher-Spin Currents and Flows in Auxiliary Field Sigma Models

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

We study local, higher-spin conserved currents in integrable $2d$ sigma models that have been deformed via coupling to auxiliary fields. These currents generate integrability-preserving flows introduced by Smirnov and Zamolodchikov. For auxiliary field (AF) deformations of a free boson, we prove that local spin-$n$ currents exist for all $n$ and give recursion relations that characterize Smirnov-Zamolodchikov (SZ) flows driven by these currents. We then show how to construct spin-$2n$ currents in a unified class of auxiliary field sigma models with common structure -- including AF theories based on the principal chiral model (PCM), its non-Abelian T-dual, (bi-)Yang-Baxter deformations of the PCM, and symmetric space models -- for interaction functions of one variable, and describe SZ flows driven by any function of the stress tensor in these cases. Finally, we give perturbative solutions for spin-$3$ SZ flows in any member of our unified class of AF models with underlying $\mathfrak{su}(3)$ algebra. Part of our analysis shows that the class of AF deformations can be extended by allowing the interaction function to depend on a larger set of variables than has previously been considered.

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Daniele Bielli, Christian Ferko, Michele Galli, Gabriele Tartaglino-Mazzucchelli. 2025-04-24. Higher-Spin Currents and Flows in Auxiliary Field Sigma Models. https://arxiv.org/abs/2504.17294

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