Exclusion Statistics in Conformal Field Theory -- generalized fermions and spinons for level-1 WZW theories

TL;DR

This paper investigates exclusion statistics of quasi-particles in conformal field theories, providing a systematic method and explicit formulas for various models including minimal models, parafermions, and WZW theories.

Contribution

It introduces a recursion-based method to analyze exclusion statistics and derives explicit expressions for finitized affine characters and spinon decompositions in multiple CFT models.

Findings

Developed a systematic recursion relation approach

Derived explicit finitized affine characters

Analyzed spinon decompositions in WZW models

Abstract

We systematically study the exclusion statistics for quasi-particles for Conformal Field Theory spectra by employing a method based on recursion relations for truncated spectra. Our examples include generalized fermions in c<1 unitary minimal models, Z_k parafermions, and spinons for the su(n)_1, so(n)_1 and sp(2n)_1 Wess-Zumino-Witten models. For some of the latter examples we present explicit expressions for finitized affine characters and for the N-spinon decomposition of affine characters.