Non-anti-commutative deformation of effective potentials in supersymmetric gauge theories Original Research Article

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 the latter. We found a non-vanishing gluino condensate in vacuum but no further dynamical supersymmetry breaking in the deformed theory.