Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 124, 15 pages      arXiv:1902.08598      https://doi.org/10.3842/SIGMA.2020.124

Further Results on a Function Relevant for Conformal Blocks

Vincent Comeau a, Jean-François Fortin b and Witold Skiba c
a) Department of Physics, McGill University, Montréal, QC H3A 2T8, Canada
b) Département de Physique, de Génie Physique et d'Optique, Université Laval, Québec, QC G1V 0A6, Canada
c) Department of Physics, Yale University, New Haven, CT 06520, USA

Received July 07, 2020, in final form November 24, 2020; Published online November 30, 2020

Abstract
We present further mathematical results on a function appearing in the conformal blocks of four-point correlation functions with arbitrary primary operators. The $H$-function was introduced in a previous article and it has several interesting properties. We prove explicitly the recurrence relation as well as the $D_6$-invariance presented previously. We also demonstrate the proper action of the differential operator used to construct the $H$-function.

Key words: special functions; conformal field theory.

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