Energy bounds condition for intertwining operators of type $B$, $C$, and $G_2$ unitary affine vertex operator algebras

TL;DR

This paper extends the energy bounds condition for intertwining operators to affine VOAs of types B, C, and G2, demonstrating their unitarity and contributing to the understanding of their modular tensor categories.

Contribution

It introduces the energy bounds condition for intertwining operators of types B, C, and G2 affine VOAs, expanding previous results beyond types A and D.

Findings

Energy bounds condition established for types B, C, and G2 affine VOAs.

Proves the unitarity of the modular tensor categories associated with these VOAs.

Extends the class of VOAs known to satisfy the energy bounds condition.

Abstract

The energy bounds condition for intertwining operators of unitary rational vertex operator algebras (VOAs) was studied, first by A.Wassermann for type $A$ affine VOAs, and later by T.Loke for $c<1$ Virasoro VOAs, and by V.Toledano-Laredo for type $D$ affine VOAs. In this paper, we extend their results to affine VOAs of type $B$, $C$, and $G_2$. As a consequence, the modular tensor categories of these unitary vertex operator algebras are unitary.