Vertex operator algebras associated to modified regular representations of the Virasoro algebra

TL;DR

This paper constructs a family of vertex operator algebras of rank 26 linked to modified regular representations of the Virasoro algebra, using BZ equations and intertwining operators, and discovers new hypergeometric identities.

Contribution

It introduces a novel construction of VOAs from Virasoro algebra representations, explicitly determines their structure, and uncovers new hypergeometric identities.

Findings

Explicit VOA structures from Virasoro representations

New hypergeometric identities derived

Construction based on BZ equations and intertwining operators

Abstract

We give an abstract construction, based on the Belavin-Polyakov-Zamolodchikov equations, of a family of vertex operator algebras of rank $26$ associated to the modified regular representations of the Virasoro algebra. The vertex operators are obtained from the tensor products of intertwining operators for a pair of Virasoro algebras. We explicitly determine the structure coefficients that yield the axioms of VOAs. In the process of our construction, we obtain new hypergeometric identities.