On $G$--modular functor

TL;DR

This paper introduces $G$-equivariant modular functors and fusion categories, extending existing concepts to incorporate finite group actions, and establishes a correspondence between these generalized notions.

Contribution

It defines $G$-equivariant modular functors and fusion categories and proves their correspondence, expanding the framework of modular functor theory.

Findings

Defined $G$-equivariant modular functor and fusion category

Established a correspondence between these notions

Extended the theory to include finite group actions

Abstract

In this paper, we extend the notion of modular functor and fusion category to what we called $G$ equivariant modular functor and $G$ equivariant fusion category, where $G$ is a finite group, and establish a correspondence between between these notions.