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

TL;DR

This paper investigates a specific non-anticommutative deformation in supersymmetric gauge theories, deriving a universal formula for the deformed superpotential and analyzing its effects on the IR physics of super-Yang-Mills theory.

Contribution

It introduces a simple non-perturbative formula for NAC-deformed superpotentials applicable to any chiral superpotential in supersymmetric gauge theories.

Findings

Deformed superpotential remains Lorentz-invariant.

Non-zero gluino condensate persists in the deformed vacuum.

No additional dynamical supersymmetry breaking occurs.

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.