Simplifications of four-point functions in N=4 supersymmetric Yang-Mills theory at two loops

TL;DR

This paper simplifies the calculation of two-loop four-point functions in N=4 supersymmetric Yang-Mills theory by using superconformal Ward identities and harmonic analyticity, reducing the problem to a known one-loop integral.

Contribution

It introduces a novel method combining superconformal Ward identities and harmonic analyticity to simplify two-loop calculations in N=4 SYM.

Findings

Two-loop four-point functions are expressed in terms of one-loop box integrals.

The simplified results are confirmed by numerical computations.

The approach streamlines complex multi-loop calculations in supersymmetric gauge theories.

Abstract

The superconformal Ward identities combined with N=2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory in terms of the well-known one-loop box integral. The result is confirmed by a direct numerical computation.