Non(anti)commutative superspace with coordinate-dependent deformation

Abstract

We consider non(anti)commutative superspace with coordinate dependent deformation parameters $C^{\alpha \beta }$. We show that a chiral $\mathcal{N}=1/2$ supersymmetry can be defined and that chiral and antichiral superfields are still closed under the Moyal-Weyl associative product implementing the deformation. A consistent $\mathcal{N}=1/2$ Super Yang-Mills deformed theory can be constructed provided $C^{\alpha \beta }$ satisfies a suitable condition which can be connected with the graviphoton background at the origin of the deformation. After adding matter we also discuss the Konishi anomaly and the gluino condensation.

References added. Accepted for publication in PRD