Virasoro completeness relation and the inverse Shapovalov form

Fortin, Jean-François; Quintavalle, Lorenzo; Skiba, Witold

doi:10.1103/PhysRevD.111.085010

Title: Virasoro completeness relation and the inverse Shapovalov form

Journal Article · 06 April 2025 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.111.085010 · OSTI ID:2550688

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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. Published by the American Physical Society 2025

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0017660

OSTI ID:: 2550688

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 8 Vol. 111; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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