### 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 |
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Pages (from-to) | 358-385 |

Number of pages | 28 |

Journal | Nuclear Physics B |

Volume | 740 |

Issue number | 3 |

DOIs | |

Publication status | Published - 24 Apr 2006 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*740*(3), 358-385. https://doi.org/10.1016/j.nuclphysb.2006.02.022