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.

Bianchi, M., Penati, S., Romagnoni, A., Siani, M. (2009). Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability. JOURNAL OF HIGH ENERGY PHYSICS, 2009(7) [10.1088/1126-6708/2009/07/039].

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

BIANCHI, MARCO STEFANO;PENATI, SILVIA;ROMAGNONI, ALBERTO;SIANI, MASSIMO VINCENZO DUILIO
2009

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.
Articolo in rivista - Articolo scientifico
Non(anti)commutative field theory, renormalization
English
Bianchi, M., Penati, S., Romagnoni, A., Siani, M. (2009). Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability. JOURNAL OF HIGH ENERGY PHYSICS, 2009(7) [10.1088/1126-6708/2009/07/039].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/9286
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