Unitarity of the modular tensor categories associated to unitary vertex operator algebras, I

TL;DR

This paper initiates the construction of a unitary structure for the modular tensor category linked to a unitary rational vertex operator algebra, laying foundational work for the series.

Contribution

It introduces the first part of a two-part series establishing unitarity of MTCs from unitary rational VOAs, a significant step in understanding their mathematical structure.

Findings

First step towards unitarity of MTCs from VOAs

Framework for constructing unitary structures in MTCs

Lays groundwork for subsequent parts of the series

Abstract

This is the first part in a two-part series of papers constructing a unitary structure for the modular tensor category (MTC) associated to a unitary rational vertex operator algebra (VOA).