Non(anti)commutative Script N = 2 supersymmetric gauge theory from superstrings in graviphoton background

We study open string amplitudes with the D3-branes in type IIB superstring theory compactified on C2/Z2. We introduce constant graviphoton background along the branes and calculate disk amplitudes using the NSR formalism. We take the zero slope limit and investigate the effective Lagrangian on the D3-branes deformed by the graviphoton background. We find that the deformed Lagrangian agrees with that of = 2 supersymmetric U(N) gauge theory defined in non(anti)commutative = 1 superspace by choosing appropriate graviphoton background. It is also shown that abelian gauge theory defined in = 2 harmonic superspace with specific non-singlet deformation is consistent with the deformed theory.