Four-point functions in N=4 supersymmetric Yang-Mills theory at two loops

TL;DR

This paper computes four-point functions in N=4 supersymmetric Yang-Mills theory at two loops, revealing non-canceling logarithmic singularities and confirming the analyticity of Green's functions for analytic operators at this order.

Contribution

It introduces a harmonic superspace perturbation approach to evaluate four-point functions at two loops in N=4 SYM, highlighting singularity behavior and operator analyticity.

Findings

Logarithmic singularities appear at two loops and do not cancel.

Green's functions of analytic operators remain analytic at this order.

Results are expressed via differential operators acting on scalar integrals.

Abstract

Four-point functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory are studied using N=2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar two loop integral. The leading singular behaviour is obtained in the limit that two of the points approach one another. We find logarithmic singularities which do not cancel out in the sum of all diagrams. It is confirmed that Green's functions of analytic operators are indeed analytic at this order in perturbation theory.