The Virasoro Completeness Relation and Inverse Shapovalov Form
High Energy Physics - Theory
2025-04-11 v2 Mathematical Physics
math.MP
Abstract
In this work, we introduce an explicit expression for the inverse of the symmetric bilinear form of Virasoro Verma modules, the so-called Shapovalov form, in terms of singular vector operators and their conformal dimensions. Our proposed expression also determines the resolution of the identity for Verma modules of the Virasoro algebra, and can be thus employed in the computation of Virasoro conformal blocks via the sewing procedure.
Cite
@article{arxiv.2409.12224,
title = {The Virasoro Completeness Relation and Inverse Shapovalov Form},
author = {Jean-François Fortin and Lorenzo Quintavalle and Witold Skiba},
journal= {arXiv preprint arXiv:2409.12224},
year = {2025}
}
Comments
8 pages, no figures; v2: Published version, clarified details on the setup and streamlined the main proof