Recursive structure of the Gau\ss{} hypergeometric function and boundary/crosscap conformal block

TL;DR

This paper explores the recursive structure of the Gauss hypergeometric function and compares it with boundary/crosscap conformal blocks, revealing a perfect pole structure match but slight differences in recursive behavior.

Contribution

It establishes a detailed comparison between the recursive structures of the Gauss hypergeometric function and conformal blocks in boundary/crosscap conformal field theories.

Findings

Pole structures match perfectly

Recursive structures are slightly 'off-shell'

Provides insights into conformal block recursion

Abstract

The Gau\ss{} hypergeometric function shows a recursive structure which resembles those found in conformal blocks. We compare it with the recursive structure of the conformal block in boundary/crosscap conformal field theories that is obtained from the representation theory. We find that the pole structure perfectly agrees but the recursive structure in the Gau\ss{} hypergeometric function is slightly ``off-shell".