Superfield covariant analysis of the divergence structure of noncommutative supersymmetric QED$_4$

TL;DR

This paper investigates the divergence structure of noncommutative supersymmetric QED$_4$ using superfield formalism, demonstrating gauge-invariant cancellation of leading divergences and gauge-dependent subleading divergences, supporting the theory's consistency.

Contribution

It extends previous one-loop results to arbitrary supersymmetries and gauges, analyzing divergence cancellations in noncommutative supersymmetric QED$_4$.

Findings

Leading UV/IR divergences cancel in all gauges.

Subleading divergences cancel only in specific gauges.

The theory remains perturbatively consistent despite divergences.

Abstract

Commutative supersymmetric Yang-Mills is known to be renormalizable for ${\cal N} = 1, 2$, while finite for ${\cal N} = 4$. However, in the noncommutative version of the model (NCSQED$_4$) the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of NCSQED$_4$ by working systematically within the covariant superfield formulation. In the Landau gauge, it has already been shown for ${\cal N} = 1$ that the gauge field two-point function is free of harmful UV/IR infrared singularities, in the one-loop approximation. Here we show that this result holds without restrictions on the number of allowed supersymmetries and for any arbitrary covariant gauge. We also investigate the divergence structure of the gauge field three-point function in the one-loop approximation. It is first proved that the cancellation of the leading UV/IR infrared divergences is a gauge invariant statement. Surprisingly, we have also found that there exist subleading harmful UV/IR infrared singularities whose cancellation only takes place in a particular covariant gauge. Thus, we conclude that these last mentioned singularities are in the gauge sector and, therefore, do not jeopardize the perturbative expansion and/or the renormalization of the theory.