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 λ 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.

Highlights

  • We are interested in a two-dimensional conformal field theory (CFT) which possesses two independent current algebras generated by Ja(z) and Ja(z) which are holomorphic and anti-G

  • In this work we investigate λ-deformed current theories based on a general semi-simple group but with a left–right asymmetry induced by the different levels in the left and right sectors of the theory

  • These left–right asymmetric theories are very interesting for several reasons. They possess a new non-trivial fixed point compared to the left–right symmetric case and there is a smooth RG flow form the undeformed current algebra theory in the UV to a new CFT in the IR (see, (2.32)), on the nature of which we gave strong arguments

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Summary

Introduction

We are interested in a two-dimensional conformal field theory (CFT) which possesses two independent current algebras generated by Ja(z) and Ja(z) which are holomorphic and anti-. The mixed three-point functions involving one current are given by These correlators are non-vanishing as long as the representations R and R are conjugate for the holomorphic and anti-holomorphic sectors separately. We will compute the two- and three-point function of currents and for primary fields in the left–right asymmetric case, but for λ = 0 From these we will extract the corresponding anomalous dimensions, OPEs, equal time commutators and classical Poisson brackets. Such correlators will be denoted by · · · λ in order to distinguish them from those evaluated at the CFT point, that is for vanishing λ

Two-point functions
Current composite operators
Three-point functions
The IR fixed point
Primary field correlators and anomalous dimensions
OPEs and Poisson structure
Conclusions
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