Multivalued Fields on the Complex Plane and Braid Group Statistics

TL;DR

This paper develops a theory of free anyons on Riemann surfaces with nonabelian symmetries, introducing a multiparametric R-matrix that generalizes Yang-Baxter equations to describe nonabelian braid statistics.

Contribution

It introduces a novel framework for free anyons with nonabelian statistics on Riemann surfaces, extending Yang-Baxter equations with multiparametric R-matrices.

Findings

Formulation of a nonabelian anyon theory on Riemann surfaces.

Introduction of a multiparametric R-matrix satisfying generalized Yang-Baxter equations.

Description of nonabelian braid group statistics in this context.

Abstract

We study in this paper a theory of free anyons associated to free conformal field theories defined on Riemann surfaces with a discrete and nonabelian group of authomorphisms. The particles are exchanged according to a nonabelian statistics, in which the $R-$matrix satisfy a multiparametric generalization of the usual Yang$-$Baxter equations.