Exact 3D Conformal Blocks from Fractional Calculus
High Energy Physics - Theory
2026-02-18 v2
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.
Keywords
Cite
@article{arxiv.2311.05375,
title = {Exact 3D Conformal Blocks from Fractional Calculus},
author = {Chaoming Song},
journal= {arXiv preprint arXiv:2311.05375},
year = {2026}
}