Renormalizability of non(anti)commutative gauge theories with N = 1/2 supersymmetry

Jul, 2003
21 pages
Published in:
  • JHEP 09 (2003) 045
e-Print:
Report number:
  • SNUST-030702

Citations per year

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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.
  • gauge field theory: Yang-Mills
  • supersymmetry: superfield
  • differential geometry: noncommutative
  • perturbation theory: higher-order
  • renormalization
  • field theory: deformation