  We study quantum aspects of field theories defined on N=1/2 superspace, where
both bosonic and fermionic coordinates are made non(anti)commutative. We
compute the one-loop effective superpotential, and we find that planar and
nonplanar contributions exhibit markedly different behavior. Planar diagrams
yield an effective superpotential proportional to N_c \Phi \log \Phi. For
nonplanar diagrams, we show that ultraviolet-infrared mixing takes place and
explain why some nonplanar diagrams are ultraviolet-divergent when bosonic
noncommutativity is turned off. Each nonplanar diagram is not expressible as a
star product of background fields, but, once resummed appropriately, they are
expressed as a star product involving open Wilson lines in superspace. The open
Wilson lines are responsible for ultraviolet-infrared mixing. We comment on an
intriguing relation of our result to the Dijkgraaf-Vafa correspondence between
gauge theories and matrix models.

High Energy Physics - Theory