Exact 3D Conformal Blocks from Fractional Calculus
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912908222398464 |
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| author | Song, Chaoming |
| author_facet | Song, Chaoming |
| contents | We uncover a striking connection between conformal blocks and fractional calculus. By employing a modified form of half-derivates, we derived explicitly the exact form of the three-dimensional conformal block, expressed as the product of two hypergeometric 4F3 functions. This result provides a rigorous proof of Hogervorst's formula, conjectured nearly a decade ago. Furthermore, we demonstrate its implications for the conformal bootstrap, potentially leading to new analytical techniques and numerical tools that deepen our understanding of conformal field theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05375 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exact 3D Conformal Blocks from Fractional Calculus Song, Chaoming High Energy Physics - Theory We uncover a striking connection between conformal blocks and fractional calculus. By employing a modified form of half-derivates, we derived explicitly the exact form of the three-dimensional conformal block, expressed as the product of two hypergeometric 4F3 functions. This result provides a rigorous proof of Hogervorst's formula, conjectured nearly a decade ago. Furthermore, we demonstrate its implications for the conformal bootstrap, potentially leading to new analytical techniques and numerical tools that deepen our understanding of conformal field theory. |
| title | Exact 3D Conformal Blocks from Fractional Calculus |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2311.05375 |