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

TL;DR

This paper demonstrates that certain non-anticommutative N=(1,1) supersymmetric theories remain finite at the quantum level, with divergences removable by field redefinitions, due to underlying Seiberg-Witten-type transformations.

Contribution

It shows the renormalizability and finiteness of non-anticommutative N=(1,1) theories with singlet deformation, highlighting their unique quantum properties.

Findings

Full effective action is one-loop exact with finitely many divergences.

Divergences vanish on-shell and can be removed by scalar field redefinitions.

Beta-function for the coupling constant is zero.

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.