Non-Anti-Commutative deformation of effective potentials in supersymmetric gauge theories

Abstract

We studied a nilpotent Non-Anti-Commutative (NAC) deformation of the effective superpotentials in supersymmetric gauge theories, caused by a constant self-dual graviphoton background. We derived the simple non-perturbative formula applicable to any NAC (star) deformed chiral superpotential. It is remarkable that the deformed superpotential is always `Lorentz'-invariant. As an application, we considered the NAC deformation of the pure super-Yang-Mills theory whose IR physics is known to be described by the Veneziano-Yankielowicz superpotential (in the undeformed case). The unbroken gauge invariance of the deformed effective action gives rise to severe restrictions on its form. We found a non-vanishing gluino condensate in vacuum but no further dynamical supersymmetry breaking in the deformed theory.

20 pages, LaTeX; small changes, additions and references added

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• On nonanticommutative N=2 sigma-models in two dimensions
• Non(anti)commutative SYM theory: Renormalization in superspace
• Non-local Wess-Zumino Model on Nilpotent Noncommutative Superspace
• Gauged Wess-Zumino Model in Noncommutative Minkowski Superspace
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• Chiral Models in Noncommutative N=1/2 Four Dimensional Superspace
• N=1/2 supersymmetric four-dimensional non-linear sigma-models from non-anti-commutative superspace
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