Construction of Modular Functors from Modular Tensor Categories

TL;DR

This paper constructs modular functors from modular tensor categories, demonstrating that the resulting functors inherit duality and unitarity properties when the categories possess these features.

Contribution

It provides a detailed method to build modular functors from modular tensor categories, extending Turaev's constructions with new properties.

Findings

Modular functors can be constructed from any modular tensor category.

The constructed functors inherit duality properties.

Unitarity and Hermitian structures are preserved in the construction.

Abstract

In this paper we follow the constructions of Turaev's book [Tu] closely, but with small modifications, to construct of a modular functor, in the sense of Kevin Walker, from any modular tensor category. We further show that this modular functor has duality and if the modular tensor category category is Hermitian or unitary, then the resulting modular functor is also Hermitian or unitary respectively.