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- Title
Sigma models with local couplings: a new integrability-RG flow connection.
- Authors
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.
- Subjects
SYMMETRIC spaces; STRING theory; DILATON
- Publication
Journal of High Energy Physics, 2020, Vol 2020, Issue 11, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP11(2020)020