Structure Constants of the Fractional Supersymmetry Chiral Algebras

TL;DR

This paper computes the structure constants of fractional supersymmetry chiral algebras in 2D conformal field theory, revealing their algebraic properties and braiding relations.

Contribution

It explicitly determines the structure constants for extended Virasoro algebras with one fractional spin current, advancing understanding of fractional supersymmetry.

Findings

Explicit structure constants computed for these algebras

Correlators satisfy non-Abelian braiding relations

Associativity constrains algebra structure

Abstract

The fractional supersymmetry chiral algebras in two-dimensional conformal field theory are extended Virasoro algebras with fractional spin currents. We show that associativity and closure of these algebras determines their structure constants in the case that the Virasoro algebra is extended by precisely one current. We compute the structure constants of these algebras explicitly and we show that correlators of the currents satisfy non-Abelian braiding relations.