Integral Transforms for Conformal Field Theories with a Boundary

TL;DR

This paper introduces a novel integral transform method, related to the Radon transform, to solve conformally invariant integrals in boundary conformal field theories, overcoming limitations of previous techniques.

Contribution

The authors develop a new integral transform approach tailored for boundary conformal field theories, including derivation of related hypergeometric function identities.

Findings

Effective solution for boundary conformal integrals

New hypergeometric function relations derived

Method improves upon previous techniques for boundary cases

Abstract

A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method makes essential use of an invertible integral transform, related to the radon transform, involving integration over planes parallel to the boundary. For successful application of this method several nontrivial hypergeometric function relations are also derived.