The one-loop effective action of noncommutative {\cal N}=4 super Yang-Mills is gauge invariant

TL;DR

This paper demonstrates that the gauge invariance of the one-loop effective action in noncommutative {\

Contribution

It reveals a cancellation mechanism ensuring gauge invariance in noncommutative {\

Findings

Nonplanar diagram contributions are not gauge invariant.

Gauge variation of four-point function is canceled by five-point function.

Mechanism guarantees gauge invariance of the one-loop effective action.

Abstract

We study the gauge transformation of the recently computed one-loop four-point function of {\cal N}=4 supersymmetric Yang-Mills theory with gauge group U(N). The contributions from nonplanar diagrams are not gauge invariant. We compute their gauge variation and show that it is cancelled by the variation from corresponding terms of the one-loop five-point function. This mechanism is general: it insures the gauge invariance of the noncommutative one-loop effective action.