Exclusion Statistics in Conformal Field Theory Spectra

TL;DR

This paper introduces a novel method to analyze exclusion statistics in Conformal Field Theory spectra, deriving generalized distribution functions that extend Fermi-Dirac statistics and applying them to various CFT models.

Contribution

It presents a new approach for studying exclusion statistics in CFTs, leading to generalized distribution functions and new insights into quasi-particle behavior.

Findings

Derived one-particle distribution functions generalizing Fermi-Dirac statistics

Identified a generalization of Gentile parafermions for $su(n)$ CFTs

Reproduced fractional exclusion statistics distributions in specific examples

Abstract

We propose a new method for investigating the exclusion statistics of quasi-particles in Conformal Field Theory (CFT) spectra. The method leads to one-particle distribution functions, which generalize the Fermi-Dirac distribution. For the simplest $su(n)$ invariant CFTs we find a generalization of Gentile parafermions, and we obtain new distributions for the simplest $Z_N$-invariant CFTs. In special examples, our approach reproduces distributions based on `fractional exclusion statistics' in the sense of Haldane. We comment on applications to fractional quantum Hall effect edge theories.