If you have a lagrangian for chiral superfields in 4 dimensions which is also invariant under SU(N) and you try to gauge the symmetry , You introduce a connection Γ so as to make Φ†ΓΦ gauge invariant under super gauge transformation. If Γ is hermitian , you have introduced vector superfields into the lagrangian coupled with the chiral superfields. Now why don't we consider cases in which Γ is not hermitian ?