Sigma models with local couplings: a new integrability-RG flow connection
File(s)
Accepted version
Author(s)
Hoare, Ben
Levine, Nat
Tseytlin, Arkady A
Type
Journal Article
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.
Date Issued
2020-11-06
Date Acceptance
2020-10-05
Citation
The Journal of High Energy Physics, 2020, 20 (11)
ISSN
1029-8479
Publisher
Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Journal / Book Title
The Journal of High Energy Physics
Volume
20
Issue
11
Copyright Statement
Open Access, ©The Author(s)
License URL
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000591049000001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Physics, Particles & Fields
Physics
Bosonic Strings
Integrable Field Theories
Sigma Models
STATIONARY
STRINGS
CHARGES
Publication Status
Published
Article Number
ARTN 20