Non-rational su(2) cosets and Liouville field theory

TL;DR

This paper introduces a non-rational level su(2) WZNW model with a continuous spectrum, proposing a connection to Liouville field theories through a coset construction, supported by analytic evidence.

Contribution

It proposes a novel non-rational su(2) WZNW model with a continuous spectrum and conjectures its relation to Liouville theories via a coset approach.

Findings

Supports the conjecture with analytic calculations

Establishes a link between non-rational su(2) models and Liouville theories

Provides a new perspective on non-unitary representations in conformal field theory

Abstract

We propose an su(2) WZNW model with a non-rational level and a continuous spectrum based on the non-unitary hermitian representations of the chiral algebra su(2)_k. It is conjectured that for this model the continuous spectra counterpart of the Goddard-Kent-Olive (GKO) coset construction yields the Liouville and the imaginary Liouville field theories. We support the conjecture by a number of nontrivial tests based on analytic calculations.