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

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

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


Nat Levine

Arkady A. Tseytlin


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.


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.

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
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2020
Issue 11
Article Number 20
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Copyright Statement
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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