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September 30, 2025Open Access

Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form

Key Points

The derived expression for the virasoro OPE and conformal blocks does not depend on singular vector forms, only on conformal weights.
Our expression shows compatibility, but differs from Zamolodchikov's h-recursion relation, indicating nuances in conformal block calculations.
We explore the implications of large central charge limits on our derived expression, highlighting important theoretical aspects.
A Mathematica notebook accompanies this work, offering a practical implementation of the derived expressions for broader research use.

Abstract

We derive expressions for the Virasoro OPE and four-point conformal blocks on the sphere via the resolution of identity recently determined in Phys. Rev. D 111, 085010 (2025), arXiv: 2409. 12224. Even though the resolution of the identity depends on Virasoro singular vectors, our expression for the blocks does not depend on their precise form, but just on their well-known conformal weights. We verify that our expression is compatible with -- but differs from -- Zamolodchikov's h-recursion relation and we also examine the impact of various large central charge limits in our formula. A Mathematica notebook with a simple implementation of our expression for the Virasoro conformal blocks is provided as an ancillary file.

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Cite This Study

Fortin et al. (Thu,) studied this question.

synapsesocial.com/papers/68dc12d38a7d58c25ebb1010 https://doi.org/https://doi.org/10.48550/arxiv.2509.09765

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