Noncommutative ${\cal N}=1,2$ super U(N) Yang-Mills: UV/IR mixing and effective action results at one loop

TL;DR

This paper investigates one-loop divergences and effective actions in noncommutative supersymmetric U(N) Yang-Mills theories, revealing UV/IR mixing effects and computing key correlation functions.

Contribution

It provides the first detailed analysis of one-loop divergences and effective actions in noncommutative ${ m N}=1,2$ super Yang-Mills theories using superspace methods.

Findings

Divergences occur only in two-point functions at one loop.

Planar and nonplanar sectors exhibit dual UV/IR divergences.

Four-point functions receive contributions from both vector and chiral matter loops.

Abstract

Noncommutative ${\cal N}=1$ and ${\cal N}=2$ supersymmetric Yang-Mills theories with gauge group U(N) are studied here using the background field method and superspace background covariant D-algebra in perturbation theory. At one loop divergences arise only in the two-point functions. They are logarithmic UV/IR divergences in the planar/nonplanar sectors that play a role dual to each other. We compute the planar and non planar contributions to the three- and four-point functions with vector external lines. We find that the three-point function vanishes, while the four-point function receives contributions both from vector and from chiral matter loops.