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arXiv · 2311.05375

Exact 3D Conformal Blocks from Fractional Calculus

Chaoming Song
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Abstract

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.

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Chaoming Song. 2023-11-09. Exact 3D Conformal Blocks from Fractional Calculus. https://doi.org/10.1103/2jmh-qdhj

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