Dynamically restoring conformal invariance in (integrable) ?-models

Integrable lambda-deformed sigma-models are characterized by an underlying current alge-bra/coset model CFT deformed, at the infinitesimal level, by current/parafermion bi-linears. We promote the deformation parameters to dynamical functions of time intro-duced 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.

Automated summary

Integrable lambda-deformed sigma-models involve the deformation of an underlying current algebra/coset model CFT at the infinitesimal level using current/parafermion bi-linears. By introducing the deformation parameters as dynamical functions of time, we aim to constrain them in a way that makes the beta-functions vanish and keeps the sigma-model conformal. Surprisingly, we have successfully achieved this scenario in several cases with single or multiple deformation parameters, solving a system of non-linear second-order ordinary differential equations that these parameters generally obey. The solutions correspond to the fixed points of the RG flow of the original sigma-model, allowing for interpolation between these fixed points as the time varies.