Defect Conformal Blocks from Appell Functions

TL;DR

This paper develops a group theoretical approach to compute defect conformal blocks in defect conformal field theory, expressing them in terms of hypergeometric functions and Appell functions for various field configurations.

Contribution

It introduces a formalism to derive defect conformal blocks involving multiple bulk and defect fields using Appell functions, extending previous methods.

Findings

Conformal blocks expressed with hypergeometric functions for simple cases.

Extension to cases with multiple bulk and defect fields using Appell functions.

Provides a systematic way to compute correlation functions in defect CFT.

Abstract

We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point functions of scalar fields. Starting from a configuration with one bulk and one defect field, for which the correlation function is determined by conformal symmetry, we explore two possibilities, adding either one additional defect or bulk field. In both cases it is possible to express the blocks in terms of classical hypergeometric functions, though the case of two bulk and one defect field requires Appell's function $F_4$.