Four-point functions in N=4 SYM

TL;DR

This paper presents a new superconformal and analytic formula for four-point functions of chiral primary multiplets in N=4 SYM, enabling analysis of their structure and non-renormalisation properties.

Contribution

It provides a compact, superconformal, and analytic formula for four-point functions valid for any charge Q, linking them to protected operators and their free forms.

Findings

The formula is valid for arbitrary Q.

Crossing symmetry reduces the number of independent functions.

Protected operators lead to partial non-renormalisation of four-point functions.

Abstract

A new derivation is given of four-point functions of charge $Q$ chiral primary multiplets in N=4 supersymmetric Yang-Mills theory. A compact formula, valid for arbitrary $Q$, is given which is manifestly superconformal and analytic in the internal bosonic coordinates of analytic superspace. This formula allows one to determine the spacetime four-point function of any four component fields in the multiplets in terms of the four-point function of the leading chiral primary fields. The leading term is expressed in terms of $1/2 Q(Q-1)$ functions of two conformal invariants and a number of single variable functions. Crossing symmetry reduces the number of independent functions, while the OPE implies that the single-variable functions arise from protected operators and should therefore take their free form. This is the partial non-renormalisation property of such four-point functions which can be viewed as a consequence of the OPE and the non-renormalisation of three-point functions of protected operators.