Parafermionic character formulae

TL;DR

This paper develops new character formulae for Z_N parafermionic theories, providing detailed insights into their field content, state basis, and singular vectors, with applications to SU(2) string functions.

Contribution

It introduces novel character formulae for Z_N parafermionic primary fields, enhancing understanding of their structure and connections to string functions.

Findings

New explicit character formulae for Z_N parafermionic fields

Detailed description of state basis and singular vectors

Connections established with SU(2) string functions

Abstract

We study various aspects of parafermionic theories such as the precise field content, a description of a basis of states (that is, the counting of independent states in a freely generated highest-weight module) and the explicit expression of the parafermionic singular vectors in completely irreducible modules. This analysis culminates in the presentation of new character formulae for the $Z_N$ parafermionic primary fields. These characters provide novel field theoretical expressions for $\su(2)$ string functions.