Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas

TL;DR

This paper uncovers extended chiral symmetries in certain conformal field theories, revealing SU(2) quantum numbers and constructing explicit free-field representations that facilitate calculations of operator product expansions.

Contribution

It introduces a new set of chiral operators with SU(2) quantum numbers and provides a free-field construction that simplifies their analysis and OPE computations.

Findings

Identification of 2j+1 chiral operators with SU(2) quantum numbers

Explicit free-field construction of these operators

Calculation of vacuum characters for the triplet models

Abstract

We study a set of chiral symmetries contained in degenerate operators beyond the `minimal' sector of the c(p,q) models. For the operators h_{(2j+2)q-1,1}=h_{1,(2j+2)p-1} at conformal weight [ (j+1)p-1 ][ (j+1)q -1 ], for every 2j \in N, we find 2j+1 chiral operators which have quantum numbers of a spin j representation of SU(2). We give a free-field construction of these operators which makes this structure explicit and allows their OPEs to be calculated directly without any use of screening charges. The first non-trivial chiral field in this series, at j=1/2, is a fermionic or para-fermionic doublet. The three chiral bosonic fields, at j=1, generate a closed W-algebra and we calculate the vacuum character of these triplet models.