Seiberg-Witten Map for Superfields on N=(1/2,0) and N=(1/2,1/2) Deformed Superspace

In this paper we construct the Seiberg-Witten maps for superfields on the theta-theta deformed superspaces with N=(1/2,0) and N=(1/2,1/2) supersymmety. We show that on the N=(1/2,0) deformed superspace there is no Seiberg-Witten map for antichiral superfields which is at the same time antichiral, local and which preserves the N=(1/2,0) supersymmetry. Solutions which break these requirements are presented. On the N=(1/2,1/2) deformed superspace we show that for the chiral gauge parameter, and therefore also for the chiral matter field, there is no chiral Seiberg-Witten map. Some other possible Seiberg-Witten maps for the superfields are presented.