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

I. L. Buchbinder·E. A. Ivanov·O. Lechtenfeld·I. B. Samsonov·B. M. Zupnik
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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.

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I. L. Buchbinder, E. A. Ivanov, O. Lechtenfeld, I. B. Samsonov, B. M. Zupnik. 2006-03-04. Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation. https://doi.org/10.1016/j.nuclphysb.2006.02.022

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