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arXiv · hep-th/0307091

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

Ruth Britto·Bo Feng·Soo-Jong Rey
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Abstract

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 Φ\log Φ. 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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Ruth Britto, Bo Feng, Soo-Jong Rey. 2003-07-16. Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines. https://doi.org/10.1088/1126-6708%2F2003%2F08%2F001

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