Towards a consistent noncommutative supersymmetric Yang-Mills theory: superfield covariant analysis

TL;DR

This paper investigates the quantum consistency of noncommutative supersymmetric Yang-Mills theories with different supersymmetry levels, analyzing one-loop corrections and divergence cancellations to assess their renormalizability and finiteness.

Contribution

It provides a superfield covariant analysis of one-loop corrections in noncommutative SYM theories, highlighting divergence cancellations specific to the fundamental representation and maximal supersymmetry.

Findings

Infrared divergences cancel only in the fundamental representation.

Planar sector UV divergences cancel in ${\cal N}=4$ theory.

Supports the UV finiteness of ${\cal N}=4$ noncommutative SYM.

Abstract

Commutative four dimensional supersymmetric Yang-Mills (SYM) is known to be renormalizable for ${\mathcal N} = 1, 2$, and finite for ${\mathcal N} = 4$. However, in the noncommutative version of the model 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 the ${\cal N} = 1, 2, 4$ noncommutative supersymmetric Yang-Mills theory with gauge group U(N) (NCSYM). We employ the covariant superfield framework to compute the one-loop corrections to the two- and three-point functions of the gauge superfield $V$. It is found that the cancellation of the harmful UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. We argue that this is in agreement with the low energy limit of the open superstring in the presence of an external magnetic field. As expected, the planar sector of the two-point function of the $V$ superfield exhibits UV divergences. They are found to cancel, in the Feynman gauge, for the maximally extended ${\cal N} = 4$ supersymmetric theory. This gives support to the belief that the ${\cal N} = 4$ NCSYM theory is UV finite.