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

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.

1+30 pages, 5 figures

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• One-loop renormalisation of N=1/2 supersymmetric gauge theory with a superpotential
• The non-anticommutative supersymmetric Wess-Zumino model
• Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory
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• The non-anticommutative supersymmetric U(1) gauge theory
• One-loop divergences in the two-dimensional non-anticommutative supersymmetric sigma-model
• Non-anticommutative solitons