Integrable deformations of the $G_{k_1} \times G_{k_2}/G_{k_1+k_2}$ coset CFTs

TL;DR

This paper investigates the integrable lambda-deformations of certain coset conformal field theories, revealing new symmetries, exact beta-functions, and IR fixed points, with results supported by both field theory and gravitational analyses.

Contribution

It provides a detailed analysis of lambda-deformations for unequal level coset CFTs, uncovering new symmetries and deriving exact beta-functions and IR fixed points.

Findings

Identified a non-trivial symmetry in the model's parameter space.

Computed the exact beta-function for the deformation parameter.

Demonstrated the IR fixed point corresponds to a different coset CFT.

Abstract

We study the effective action for the integrable $\lambda$-deformation of the $G_{k_1} \times G_{k_2}/G_{k_1+k_2}$ coset CFTs. For unequal levels theses models do not fall into the general discussion of $\lambda$-deformations of CFTs corresponding to symmetric spaces and have many attractive features. We show that the perturbation is driven by parafermion bilinears and we revisit the derivation of their algebra. We uncover a non-trivial symmetry of these models parametric space, which has not encountered before in the literature. Using field theoretical methods and the effective action we compute the exact in the deformation parameter $\beta$-function and explicitly demonstrate the existence of a fixed point in the IR corresponding to the $G_{k_1-k_2} \times G_{k_2}/G_{k_1}$ coset CFTs. The same result is verified using gravitational methods for $G=SU(2)$. We examine various limiting cases previously considered in the literature and found agreement.