Covariant quantization of N=1/2 SYM theories and supergauge invariance

So far, quantum properties of N=1/2 nonanticommutative (NAC) superYang--Mills theories have been investigated in the WZ gauge. The gaugeindependence of the results requires assuming that at the quantum levelsupergauge invariance is not broken by nonanticommutative geometry. In thispaper we use an alternative approach which allows studying these theories in amanifestly gauge independent superspace setup. This is accomplished bygeneralizing the background field method to the NAC case, by moving to amomentum superspace where star products are treated as exponential factors andby developing momentum supergraph techniques. We compute the one--loop gaugeeffective action for NAC U(N) gauge theories with matter in the adjointrepresentation. Despite the appearance of divergent contributions which break(super)gauge invariance, we prove that the effective action at this order isindeed invariant.Comment: 24 pages, 3 figures, some references adde