Projections of Virasoro Singular Vectors

TL;DR

This paper utilizes explicit formulas for Virasoro singular vectors to rigorously analyze their action on conformal fields, advancing the mathematical understanding of fusion in conformal field theory.

Contribution

It provides constructive proofs of key results on Virasoro singular vectors and their role in conformal field theory, based on explicit formulae.

Findings

Explicit formulas for Virasoro singular vectors

Rigorous description of singular vectors' action on conformal fields

Enhanced understanding of fusion processes in conformal field theory

Abstract

We use recently derived explicit formulae for the Virasoro algebra's singular vectors to give constructive proofs of three results due to Feigin and Fuchs. The main result, which is needed for a rigorous treatment of fusion, describes the action of the singular vectors on conformal fields.