$\lambda$-deformations of left-right asymmetric CFTs

TL;DR

This paper analyzes $ ext{lambda}$-deformations of asymmetric current algebra conformal field theories, revealing a new IR fixed point and deriving exact correlators, OPEs, and Poisson brackets to understand the IR CFT structure.

Contribution

It provides the first all-loop anomalous dimensions and exact correlators for deformed asymmetric current algebra theories with different levels, identifying a novel IR fixed point.

Findings

Discovery of a new non-trivial IR fixed point.

Exact two- and three-point functions computed.

Deformation of Poisson brackets from isotropic PCM structure.

Abstract

We compute the all-loop anomalous dimensions of current and primary field operators in deformed current algebra theories based on a general semi-simple group, but with different (large) levels for the left and right sectors. These theories, unlike their equal level counterparts, possess a new non-trivial fixed point in the IR. By computing the exact in $\lambda$ two- and three-point functions for these operators we deduce their OPEs and their equal-time commutators. Using these we argue on the nature of the CFT at the IR fixed point. The associated to the currents Poisson brackets are a two-parameter deformation of the canonical structure of the isotropic PCM.