Non(anti)commutative superspace with coordinate-dependent deformation

Abstract

We consider non(anti)commutative superspace with coordinate-dependent deformation parameters C^αβ . We show that a chiral 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 N = 1/2 super Yang-Mills deformed theory can be constructed provided C^αβ 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.