Extended multiplet structure in Logarithmic Conformal Field Theories

TL;DR

This paper investigates the extended multiplet structures in logarithmic conformal field theories derived from SU(2)_k quantum Hamiltonian reduction, revealing new multiplet formations and conjecturing their role in rational models.

Contribution

It explicitly calculates correlators in c_{p,q} models, discovering additional multiplet structures beyond minimal sectors, including fermionic and triplet fields, and proposes their significance in extended rational models.

Findings

Discovery of extra non-chiral fermionic fields at specific null vector levels.

Identification of a chiral triplet of fields at a particular conformal weight.

Conjecture that the triplet algebra may lead to rational extended c_{p,q} models.

Abstract

We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may produce a rational extended c_{p,q} model. We also find a doublet of fields at h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic.