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

TL;DR

This paper investigates quantum effects in non(anti)commutative superspace, revealing how UV/IR mixing and open Wilson lines influence the effective superpotential, with implications for gauge theories and matrix models.

Contribution

It introduces a detailed analysis of one-loop effective superpotentials in non(anti)commutative superspace, highlighting the role of open Wilson lines in UV/IR mixing and nonplanar diagram behavior.

Findings

Planar diagrams produce a superpotential proportional to N_c    log .

Nonplanar diagrams exhibit UV/IR mixing and some are UV-divergent without bosonic noncommutativity.

Resummed nonplanar diagrams can be expressed as star products involving open Wilson lines.

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 \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.