SU(2)_k Logarithmic Conformal Field Theories

TL;DR

This paper explores the structure of SU(2)_k WZNW models, especially SU(2)_0, revealing their nature as logarithmic conformal field theories with indecomposable representations, extended algebras, and connections to the c=-2 triplet model.

Contribution

It demonstrates that SU(2)_0 models are examples of LCFTs with indecomposable representations and extended algebras, and develops techniques for analyzing correlators via quantum Hamiltonian reduction.

Findings

SU(2)_0 models exhibit logarithmic CFT features with indecomposable representations.

Explicit construction of chiral fields generating extended algebras in SU(2)_0.

Quantum Hamiltonian reduction relates SU(2)_0 to the c=-2 triplet model.

Abstract

We analyse the SU(2)_k WZNW models beyond the integrable representations and in particular the case of SU(2)_0. We find that these are good examples of logarithmic conformal field theories as indecomposable representations are naturally produced in the fusion of discrete irreducible representations. We also find extra, chiral and non-chiral, multiplet structure in the theory. The chiral fields, which we construct explicitly in SU(2)_0, generate extended algebras within the model. We also study the process of quantum hamiltonian reduction of SU(2)_0, giving the c=-2 triplet model, in both the free field approach and at the level of correlation functions. For rational level SU(2)_k this gives us a useful technique to study the h_{1,s} correlators of the c_{p,q} models and we find very similar structures to SU(2)_0. We also discuss LCFT as a limit of a sequence of ordinary CFTs and some of the subtleties that can occur.