One-loop four-point function in noncommutative {\cal N}=4 Yang-Mills theory

TL;DR

This paper calculates the one-loop four-point function in noncommutative { m N}=4 supersymmetric Yang-Mills theory, revealing that nonplanar contributions break gauge invariance at the quantum level.

Contribution

It provides the first detailed off-shell computation of the one-loop four-point function in noncommutative { m N}=4 SYM using { m N}=1 superspace and background field methods.

Findings

Nonplanar contributions break gauge invariance.

The low-energy approximation simplifies the effective action.

Complete off-shell contributions are obtained from supergraphs.

Abstract

We compute the one-loop four-point function in {\cal N}=4 supersymmetric Yang-Mills theory with gauge group U(N). We perform the calculation in {\cal N}=1 superspace using the background field method and obtain the complete off-shell contributions to the effective action from planar and non planar supergraphs. In the low-energy approximation the result simplifies and we can study its properties under gauge transformations. It appears that the nonplanar contributions do not maintain the gauge invariance of the classical action.