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arXiv · hep-th/0307275

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

Oleg Lunin·Soo-Jong Rey
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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.

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Oleg Lunin, Soo-Jong Rey. 2003-08-14. Renormalizability of Non(anti)commutative Gauge Theories with N=1/2 Supersymmetry. https://doi.org/10.1088/1126-6708%2F2003%2F09%2F045

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