Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability

TL;DR

This paper investigates the renormalization and stability of nonanticommutative supersymmetric U(1) gauge theories with matter, revealing that nonanticommutativity destabilizes fixed points and affects the theories' infrared behavior.

Contribution

It provides a complete one-loop renormalization analysis for nonanticommutative U*(1) SYM theories with matter and explores their fixed points and stability, extending to SU(3) flavor cases.

Findings

NAC U(1) SYM theories are one-loop finite with a cubic superpotential.

Deforming superpotentials leads to non-vanishing beta-functions.

Nonanticommutativity destabilizes fixed points in the RG flow.

Abstract

Renormalizable nonanticommutative SYM theories with chiral matter in the adjoint representation of the gauge group have been recently constructed in [arXiv:0901.3094]. In the present paper we focus on the U*(1) case with matter interacting through a cubic superpotential. For a single flavor, in a superspace setup and manifest background covariant approach we perform the complete one-loop renormalization and compute the beta-functions for all couplings appearing in the action. We then generalize the calculation to the case of SU(3) flavor matter with a cubic superpotential viewed as a nontrivial NAC generalization of the ordinary abelian N=4 SYM and its marginal deformations. We find that, as in the ordinary commutative case, the NAC N=4 theory is one-loop finite. We provide general arguments in support of all-loop finiteness. Instead, deforming the superpotential by marginal operators gives rise to beta-functions which are in general non-vanishing. We study the spectrum of fixed points and the RG flows. We find that nonanticommutativity always makes the fixed points unstable.