Higher-Spin Currents and Flows in Auxiliary Field Sigma Models

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Main Authors: Bielli, Daniele, Ferko, Christian, Galli, Michele, Tartaglino-Mazzucchelli, Gabriele
Format: Preprint
Published: 2025
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author Bielli, Daniele
Ferko, Christian
Galli, Michele
Tartaglino-Mazzucchelli, Gabriele
author_facet Bielli, Daniele
Ferko, Christian
Galli, Michele
Tartaglino-Mazzucchelli, Gabriele
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_17294
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Higher-Spin Currents and Flows in Auxiliary Field Sigma Models
Bielli, Daniele
Ferko, Christian
Galli, Michele
Tartaglino-Mazzucchelli, Gabriele
High Energy Physics - Theory
Mathematical Physics
Exactly Solvable and Integrable Systems
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.
title Higher-Spin Currents and Flows in Auxiliary Field Sigma Models
topic High Energy Physics - Theory
Mathematical Physics
Exactly Solvable and Integrable Systems
url https://arxiv.org/abs/2504.17294