document: There exist some interesting cases where the deformation structure becomes simple. One is the limit to the N=1/2 superspace [5], where the action should reduce to N=1/2 super-Yang–Mills theory with adjoint matter. Another interesting case is the singlet deformation [10,11], where the deformation parameters belongs to the singlet representation of the R-symmetry group SU(2)R. In this Letter, we will study N=2 supersymmetric U(1) gauge theory in the harmonic superspace with singlet deformation. In this case, the gauge and supersymmetry transformations get correction linear in the deformation parameter. Therefore we can easily perform the field redefinition such that the component fields transform canonically under the gauge transformation. In the case of N=1/2 super-Yang–Mills theory, such field redefinition is also possible [5]. But in this case the component fields do not transform canonically under the deformed supersymmtery transformation. In the singlet case, we will show that there is a field redefinition such that the redefined fields also transform canonically under the deformed supersymmetry. We will construct a deformed Lagrangian which is invariant under both the gauge and supersymmetry transformations. We find that the deformed Lagrangian is characterized by a single function of an antiholomorphic scalar field.
doc_bio_tags: O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O B I O O O O O O O O O O O O O O O O O O B I O B I O O O O B I I I O B I O O B I O O O O O O B I O O O B I O O O O B I O O O O O O O O B I O O O O O O O O O B I O O O O O O B I I O O B I O O O O O O O B I O O O O O O O O O O B I O O O O B I O O O O O O B I I I O O O O B I O O O O B I O O B I I