Dr Ben Hoare ben.hoare@durham.ac.uk
Associate Professor
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. 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 |
Published Journal Article
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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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