Virasoro completeness relation and the inverse Shapovalov form
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.
Authors
- Jean-François Fortin (ORCID: https://orcid.org/0000-0002-7813-5015)
- Witold Skiba (ORCID: https://orcid.org/0000-0002-2800-4148)
- Lorenzo Quintavalle (ORCID: https://orcid.org/0000-0002-2768-0419)
Institutions
- Yale University (US)
- Université Laval (CA)
Publication Details
- Journal
- Physical review. D/Physical review. D.
- Published
- 2025-04-07
- DOI
- https://doi.org/10.1103/physrevd.111.085010
- Citations
- 1
- Primary Topic
- Algebraic structures and combinatorial models
- Type
- article
- Field-Weighted Citation Impact
- 4.09
Funders
- U.S. Department of Energy
- Natural Sciences and Engineering Research Council of Canada