A renormalizable N=1/2 SYM theory with interacting matter

TL;DR

This paper develops a one-loop renormalizable N=1/2 supersymmetric gauge theory with interacting matter, overcoming previous non-renormalizability issues by modifying the action and couplings.

Contribution

It introduces a modified action for nonanticommutative SYM with matter that is one-loop renormalizable and preserves N=1/2 supersymmetry and gauge invariance.

Findings

The original star product approach is not renormalizable.

Modifying the quadratic action and adding couplings achieves renormalizability.

Interacting matter can be consistently included in NAC gauge theories.

Abstract

We consider nonanticommutative SYM theories with chiral matter in the adjoint representation of the SU(N) x U(1) gauge group. In a superspace setup and manifest background covariant approach we investigate the one-loop renormalization of the theory when a cubic superpotential is present. The structure of the divergent terms reveals that the theory simply obtained from the ordinary one by trading products for star products is not renormalizable. Moreover, because of the different renormalization undergone by the abelian field compared to the non-abelian ones, the superpotential seems to be incompatible with the requests of renormalizability, gauge and N=1/2 invariance. However, by a suitable modification of the quadratic action for the U(1) (anti)chiral superfields and the addition of extra couplings, we find an action which is one-loop renormalizable and manifestly N=1/2 supersymmetric and supergauge invariant. We conclude that interacting matter can be safely introduced in NAC gauge theories, in contrast with previous results.