Exclusion statistics in conformal field theory and the UCPF for WZW models

TL;DR

This paper explores fractional exclusion statistics within conformal field theory, emphasizing the role of null quasi-particles in WZW models and connecting these ideas to the Universal Chiral Partition Function.

Contribution

It extends the understanding of exclusion statistics in conformal field theory by identifying the necessity of null quasi-particles alongside pseudo-particles.

Findings

Null quasi-particles are essential for accounting null-states in WZW models.

The connection between exclusion statistics and the Universal Chiral Partition Function is clarified.

Examples demonstrate the application of these concepts in specific WZW-models.

Abstract

In this paper we further elaborate on the notion of fractional exclusion statistics, as introduced by Haldane, in two-dimensional conformal field theory, and its connection to the Universal Chiral Partition Function as defined by McCoy and collaborators. We will argue that in general, besides the pseudo-particles introduced recently by Guruswamy and Schoutens, one needs additional `null quasi-particles' to account for the null-states in the quasi-particle Fock space. We illustrate this in several examples of WZW-models.