Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines

Details Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines

2003-07-09

arxiv.org/abs/hep-th/0307091v2

JHEP 0308 (2003) 001

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 1 figure; V2: references added

Scientific paper

10.1088/1126-6708/2003/08/001

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.

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