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<p>We study local, higher-spin conserved currents in integrable 2<i>d</i> 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-<i>n</i> currents exist for all <i>n</i> and give recursion relations that characterize Smirnov-Zamolodchikov (SZ) flows driven by these currents. We then show how to construct spin-2<i>n</i> 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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26937_Article_IEq1.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="fraktur">su</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathfrak{su} \)</EquationSource> </InlineEquation>(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.</p>

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Higher-spin currents and flows in auxiliary field sigma models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月12日

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  • Daniele Bielli,
  • Christian Ferko,
  • Michele Galli,
  • Gabriele Tartaglino-Mazzucchelli

摘要

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 su \( \mathfrak{su} \) (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.