SciPost Submission Page
Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form
by Jean-François Fortin, Lorenzo Quintavalle, Witold Skiba
Submission summary
| Authors (as registered SciPost users): | Lorenzo Quintavalle |
| Submission information | |
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| Preprint Link: | scipost_202510_00002v1 (pdf) |
| Date submitted: | Oct. 2, 2025, 6:06 p.m. |
| Submitted by: | Lorenzo Quintavalle |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing