Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation

Abstract

We study the quantum properties of two theories with a non-anticommutative (or nilpotent) chiral singlet deformation of N=(1,1) supersymmetry: the abelian model of a vector gauge multiplet and the model of a gauge multiplet interacting with a neutral hypermultiplet. In spite of the presence of a negative-mass-dimension coupling constant (deformation parameter), both theories are shown to be finite in the sense that the full effective action is one-loop exact and contains finitely many divergent terms, which vanish on-shell. The beta-function for the coupling constant is equal to zero. The divergencies can all be removed off shell by a redefinition of one of the two scalar fields of the gauge multiplet. These notable quantum properties are tightly related to the existence of a Seiberg-Witten-type transformation in both models.

1+31 pages, 2 figures, uses axodraw.sty; v2: a misprint corrected; v3: a reference added; v.4: minor changes in the text, references added, published version

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• Non-anticommutative deformation of N=(1,1) hypermultiplets
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Cited by in corpus (6)

• Cryptoreality of nonanticommutative Hamiltonians
• Non-singlet Q-deformed N=(1,0) and N=(1,1/2) U(1) actions
• A renormalizable N=1/2 SYM theory with interacting matter
• Gauge theory in deformed N=(1,1) superspace
• Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability
• Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model