Extended chiral algebras in the SU(2)_0 WZNW model

TL;DR

This paper explores extended chiral algebras in the SU(2)_0 WZNW model, revealing their structure, representations, and connections to rational conformal field theories, with explicit algebraic and correlation function analyses.

Contribution

It introduces and analyzes extended W-algebras in the SU(2)_0 WZNW model, including free field representations and their relation to c=-2 models.

Findings

Extended W-algebras are similar to c=-2 models but with additional Kac-Moody structure.

Explicit free field representations for j=2 and j=3 operators are provided.

The algebra's associativity depends on null vector decoupling, suggesting quasi-rational CFTs.

Abstract

We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure. Moreover on Hamiltonian reduction these SU(2)_0 W-algebras exactly reduce to those found in c=-2. We explicitly find the free field representations for the chiral j=2 and j=3 operators which have respectively a fermionic doublet and bosonic triplet nature. The correlation functions of these operators accounts for the rational solutions of the Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full algebra of the j=2 operators and find that the associativity of the algebra is only guaranteed if certain null vectors decouple from the theory. We conjecture that these algebras may produce a quasi-rational conformal field theory.