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

Hoare, Ben; Levine, Nat; Tseytlin, Arkady A.

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.

Citation

Hoare, B., Levine, N., & Tseytlin, A. A. (2020). Sigma models with local couplings: a new integrability-RG flow connection. Journal of High Energy Physics, 2020(11), Article 20. https://doi.org/10.1007/jhep11%282020%29020

• Journal Article Type: Article
• Acceptance Date: Oct 5, 2020
• Online Publication Date: Nov 6, 2020
• Publication Date: 2020-11
• Deposit Date: Sep 13, 2021
• Publicly Available Date: Sep 28, 2021
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2020
• Issue: 11
• Article Number: 20
• DOI: https://doi.org/10.1007/jhep11%282020%29020
• Public URL: https://durham-repository.worktribe.com/output/1250711
• Related Public URLs: https://arxiv.org/abs/2008.01112