The exact $C$-function in integrable $\lambda$-deformed theories

TL;DR

This paper computes the exact C-function for a broad class of integrable lambda-deformed theories using CFT techniques, confirming their RG flow properties align with Zamolodchikov's c-theorem.

Contribution

It provides explicit formulas for the exact C-function in lambda-deformed current algebra and coset CFTs, advancing understanding of their RG flows.

Findings

Derived exact C-functions obey Zamolodchikov's c-theorem.

Explicit RG flow analysis for asymmetric current algebra deformations.

Confirmed integrability and conformal properties across deformations.

Abstract

By employing CFT techniques, we show how to compute in the context of \lambda-deformations of current algebras and coset CFTs the exact in the deformation parameters C-function for a wide class of integrable theories that interpolate between a UV and an IR point. We explicitly consider RG flows for integrable deformations of left-right asymmetric current algebras and coset CFTs. In all cases, the derived exact C-functions obey all the properties asserted by Zamolodchikov's c-theorem in two-dimensions.