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

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. (author)