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

T. Hatanaka·S. V. Ketov·Y. Kobayashi·S. Sasaki
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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.

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T. Hatanaka, S. V. Ketov, Y. Kobayashi, S. Sasaki. 2005-02-08. Non-Anti-Commutative deformation of effective potentials in supersymmetric gauge theories. https://doi.org/10.1016/j.nuclphysb.2005.03.009

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