# The most general $\lambda$-deformation of CFTs and integrability

## TL;DR

This paper introduces a broad class of integrable deformations of multi-WZW models with arbitrary levels, deriving their effective actions, RG flows, and fixed points, thus advancing understanding of integrable flows between conformal field theories.

## Contribution

It presents the most general integrable deformation of multi-WZW models with explicit all-loop effective action and RG flow equations, including non-Abelian T-duality limits.

## Key findings

- Derived all-loop effective action for the deformed models.
- Obtained exact RG flow equations and classified fixed points.
- Identified models as realizations of integrable flows between CFTs.

## Abstract

We show that the CFT with symmetry group $G_{k_1}\times G_{k_2}\times \cdots \times G_{k_n}$ consisting of WZW models based on the same group $G$, but at arbitrary integer levels, admits an integrable deformation depending on $2(n-1)$ continuous parameters. We derive the all-loop effective action of the deformed theory and prove integrability. We also calculate the exact in the deformation parameters RG flow equations which can be put in a particularly simple compact form. This allows a full determination and classification of the fixed points of the RG flow, in particular those that are IR stable. The models under consideration provide concrete realizations of integrable flows between CFTs. We also consider non-Abelian T-duality type limits.