Renormalizability of Non(anti)commutative Gauge Theories with N=1/2 Supersymmetry

Abstract

Non(anti)commutative gauge theories are supersymmetric Yang-Mills and matter system defined on a deformed superspace whose coordinates obey non(anti)commutative algebra. We prove that these theories in four dimensions with N=1/2 supersymmetry are renormalizable to all orders in perturbation theory. Our proof is based on operator analysis and symmetry arguments. In a case when the Grassman-even coordinates are commutative, deformation induced by non(anti)commutativity of the Grassman-odd coordinates contains operators of dimension-four or higher. Nevertheless, they do not lead to power divergences in a loop diagram because of absence of operators Hermitian-conjugate to them. In a case when the Grassman-even coordinates are noncommutative, the ultraviolet-infrared mixing makes the theory renormalizable by the planar diagrams, and the deformed operators are not renormalized at all. We also elucidate relation at quantum level between non(anti)commutative deformation and N=1/2 supersymmetry. We point out that the star product structure dictates a specific relation for renormalization among the deformed operators.

21 pages, Latex, 2 figs; v2. minor corrections

References in corpus (5)

• Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory
• Superstrings in Graviphoton Background and N=1/2+3/2 Supersymmetry
• Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model
• Deformed Superspace, N=1/2 Supersymmetry and (Non)Renormalization Theorems
• Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines

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