Dynamically restoring conformal invariance in (integrable) $\sigma$-models

Abstract

Integrable $\lambda$-deformed $\sigma$-models are characterized by an underlying current algebra/coset model CFT deformed, at the infinitesimal level, by current/parafermion bilinears. We promote the deformation parameters to dynamical functions of time introduced as an extra coordinate. It is conceivable that by appropriately constraining them, the beta-functions vanish and consequently the $\sigma$-model stays conformal. Remarkably, we explicitly materialize this scenario in several cases having a single and even multiple deformation parameters. These generically obey a system of non-linear second-order ordinary differential equations. They are solved by the fixed points of the RG flow of the original $\sigma$-model. Moreover, by appropriately choosing initial conditions we may even interpolate between the RG fixed points as the time varies from the far past to the far future.Finally, we present an extension of our analysis to the Yang--Baxter deformed PCMs.

v1:1+37 pages, Latex, v2: SciPost version

References in corpus (9)

• Integrable Deformations of Strings on Symmetric Spaces
• Spacetimes for λ-deformations
• The all-loop non-Abelian Thirring model and its RG flow
• On sigma model RG flow, "central charge" action and Perelman's entropy
• Integrable flows between exact CFTs
• Integrable deformations of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs
• RG flows for $\lambda$-deformed CFTs
• Weyl anomaly and the $C$-function in $\lambda$-deformed CFTs
• A free field perspective of $\lambda$-deformed coset CFT's