Energy bounds condition for intertwining operators of types 𝐵, 𝐶, and 𝐺₂ unitary affine vertex operator algebras

Abstract

The energy bounds condition for intertwining operators of unitary rational vertex operator algebras (VOAs) was studied, first by A. Wassermann for type A A affine VOAs, and later by T. Loke for c > 1 c>1 Virasoro VOAs, and by V. Toledano-Laredo for type D D affine VOAs. In this paper, we extend their results to affine VOAs of types B B , C C , and G 2 G_2 . As a consequence, the modular tensor categories of these unitary vertex operator algebras are unitary.