Renormalizability of nonanticommutative 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 nonanticommutative (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 β-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.

Original language	English
Pages (from-to)	358-385
Number of pages	28
Journal	Nuclear Physics B
Volume	740
Issue number	3
DOIs	https://doi.org/10.1016/j.nuclphysb.2006.02.022
Publication status	Published - 24 Apr 2006

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ASJC Scopus subject areas

Nuclear and High Energy Physics

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Buchbinder, I. L., Ivanov, E. A., Lechtenfeld, O., Samsonov, I. B., & Zupnik, B. M. (2006). Renormalizability of nonanticommutative N = (1,1) theories with singlet deformation. Nuclear Physics B, 740(3), 358-385. https://doi.org/10.1016/j.nuclphysb.2006.02.022

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AU - Buchbinder, I. L.

AU - Ivanov, E. A.

AU - Lechtenfeld, O.

AU - Samsonov, I. B.

AU - Zupnik, B. M.

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N2 - We study the quantum properties of two theories with a nonanticommutative (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 β-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.

AB - We study the quantum properties of two theories with a nonanticommutative (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 β-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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Access to Document

10.1016/j.nuclphysb.2006.02.022