Non(anti)commutative Superspace, UV/IR Mixing & 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 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.

20 pages, 1 figure; V2: references added

References in corpus (3)

• Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory
• Superstrings in Graviphoton Background and N=1/2+3/2 Supersymmetry
• Deformed Superspace, N=1/2 Supersymmetry and (Non)Renormalization Theorems

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• Vertex Operators for Closed Superstrings
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• Fuzzy Supersphere and Supermonopole
• Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
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• Gauge Theory on Noncommutative Supersphere from Supermatrix Model
• One-loop renormalisation of general N=1/2 supersymmetric gauge theory
• D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace
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• Chiral Models in Noncommutative N=1/2 Four Dimensional Superspace
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• The non-anticommutative supersymmetric Wess-Zumino model
• Extending general covariance: Moyal-type noncommutative manifolds
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• Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation
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• A renormalizable N=1/2 SYM theory with interacting matter
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• (Non)renormalizability of the D-deformed Wess-Zumino model
• One-loop divergences in the two-dimensional non-anticommutative supersymmetric sigma-model
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