Non(anti)commutative superspace, UV/IR mixing & open Wilson lines

We study quantum aspects of field theories defined on N=1/2 superspace, whereboth bosonic and fermionic coordinates are made non(anti)commutative. Wecompute the one-loop effective superpotential, and we find that planar andnonplanar contributions exhibit markedly different behavior. Planar diagramsyield an effective superpotential proportional to N_c \Phi \log \Phi. Fornonplanar diagrams, we show that ultraviolet-infrared mixing takes place andexplain why some nonplanar diagrams are ultraviolet-divergent when bosonicnoncommutativity is turned off. Each nonplanar diagram is not expressible as astar product of background fields, but, once resummed appropriately, they areexpressed as a star product involving open Wilson lines in superspace. The openWilson lines are responsible for ultraviolet-infrared mixing. We comment on anintriguing relation of our result to the Dijkgraaf-Vafa correspondence betweengauge theories and matrix models.Comment: 20 pages, 1 figure; V2: references adde