Composite fields, generalized hypergeometric functions and the $U(1)_Y$ symmetry in the AdS/CFT correspondence

TL;DR

This paper explores composite fields in conformal field theory and AdS/CFT, utilizing generalized hypergeometric functions to analyze four-point functions and proving a $U(1)_Y$ symmetry identity.

Contribution

It introduces a novel method of representing Green functions with hypergeometric functions and establishes a $U(1)_Y$ symmetry identity in four-point functions.

Findings

Representation of Green functions via hypergeometric functions

Proof of $U(1)_Y$ symmetry identity for four-point functions

Application of techniques to both flat CFT and AdS/CFT contexts

Abstract

We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of $U(1)_Y$ symmetry for four-point functions.