On Certain Two Dimensional Integrals that Appear In Conformal Field Theory

TL;DR

This paper generalizes a theorem for 2D Fourier transforms with holomorphic and anti-holomorphic integrands and derives conformal integrals involving hypergeometric functions, relevant to QCD triple Pomeron vertex.

Contribution

It introduces a generalized theorem for 2D Fourier transforms and derives new conformal integrals involving hypergeometric functions, applicable to QCD.

Findings

Generalized a theorem for holomorphic × anti-holomorphic integrands in 2D Fourier transforms.

Derived p-uple conformal integrals with hypergeometric functions.

Identified the case p=3 as relevant to the triple Pomeron vertex in QCD.

Abstract

In a first part, we generalize a theorem for an holomorphic $\times $ anti-holomorphic integrand, in the case of 2 dimensional Fourier transform. In the second part, we derive p-uple conformal integrals the integrand of which are linear combination of holomorphic times holomorphic generalized hypergeometric functions. The specific case $p=3$ is relevant to determine the triple Pomeron vertex in QCD.