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Sigma models with local couplings: a new integrability-RG flow connection

A preprint version of the article is available at arXiv.

Abstract

We consider several classes of σ-models (on groups and symmetric spaces, η-models, -models) with local couplings that may depend on the 2d coordinates, e.g. on time τ . We observe that (i) starting with a classically integrable 2d σ-model, (ii) formally promoting its couplings hα to functions hα(τ ) of 2d time, and (iii) demanding that the resulting time-dependent model also admits a Lax connection implies that hα(τ ) must solve the 1-loop RG equations of the original theory with τ interpreted as RG time. This provides a novel example of an ‘integrability-RG flow’ connection. The existence of a Lax connection suggests that these time-dependent σ-models may themselves be understood as integrable. We investigate this question by studying the possibility of constructing non-local and local conserved charges. Such σ-models with D-dimensional target space and time-dependent couplings subject to the RG flow naturally appear in string theory upon fixing the light-cone gauge in a (D + 2)-dimensional conformal σ-model with a metric admitting a covariantly constant null Killing vector and a dilaton linear in the null coordinate.

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Correspondence to Arkady A. Tseytlin.

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Hoare, B., Levine, N. & Tseytlin, A.A. Sigma models with local couplings: a new integrability-RG flow connection. J. High Energ. Phys. 2020, 20 (2020). https://doi.org/10.1007/JHEP11(2020)020

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Keywords

  • Bosonic Strings
  • Integrable Field Theories
  • Sigma Models