On the consistency of the three-dimensional noncommutative supersymmetric Yang-Mills theory

TL;DR

This paper investigates the quantum corrections in three-dimensional noncommutative supersymmetric Yang-Mills theory, revealing that divergence cancellations occur only in the fundamental representation and that certain divergences vanish at one-loop level.

Contribution

It demonstrates the representation-dependent cancellation of divergences and the vanishing of specific divergences at one-loop in noncommutative supersymmetric Yang-Mills theory.

Findings

Divergence cancellation occurs only in the fundamental representation.

One-loop UV and UV/IR infrared divergences vanish.

The study clarifies divergence behavior in noncommutative supersymmetric gauge theories.

Abstract

We study the one-loop quantum corrections to the U(N) noncommutative supersymmetric Yang-Mills theory in three spacetime dimensions (NCSYM$_3$). We show that the cancellation of the dangerous UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. Furthermore, in the one-loop approximation, the would be subleading UV and UV/IR infrared divergences are shown to vanish.