Parafermionic quasi-particle basis and fermionic-type characters

TL;DR

This paper introduces a new basis for highest-weight modules in parafermionic conformal theories, leading to fermionic sum representations of characters with natural combinatorial interpretation.

Contribution

It presents a novel basis for modules in parafermionic theories and derives fermionic character formulas with a clear combinatorial understanding.

Findings

Fermionic sum representations of characters are obtained.

The basis avoids singular-vector subtractions.

Combinatorics relate to Andrews-Gordon identities.

Abstract

A new basis of states for highest-weight modules in $\ZZ_k$ parafermionic conformal theories is displayed. It is formulated in terms of an effective exclusion principle constraining strings of $k$ fundamental parafermionic modes. The states of a module are then built by a simple filling process, with no singular-vector subtractions. That results in fermionic-sum representations of the characters, which are exactly the Lepowsky-Primc expressions. We also stress that the underlying combinatorics -- which is the one pertaining to the Andrews-Gordon identities -- has a remarkably natural parafermionic interpretation.