Abstract
We consider non(anti)commutative superspace with coordinate-dependent deformation parameters ${C}^{\ensuremath{\alpha}\ensuremath{\beta}}$. 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 ${C}^{\ensuremath{\alpha}\ensuremath{\beta}}$ 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.
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