Non-anticommutative deformation of N=(1,1) hypermultiplets

Abstract

We study the SO(4)×SU(2) invariant and N =(1, 0) supersymmetry-preserving nilpotent (non-anticommutative) Moyal deformation of hypermultiplets interacting with an abelian gauge multiplet, starting from their off-shell formulation in Euclidean N =(1, 1) harmonic superspace. The deformed version of a neutral or a charged hypermultiplet corresponds to the 'adjoint' or the 'fundamental' representation of the deformed U(1) gauge group on the superfields involved. The neutral hypermultiplet action is invariant under N =(2, 0) supersymmetry and describes a deformed N =(2, 2) gauge theory. For both the neutral and the charged hypermultiplet we present the corresponding component actions and explicitly give the Seiberg-Witten-type transformations to the undeformed component fields. Mass terms and scalar potentials for the hypermultiplets can be generated via the Scherk-Schwarz mechanism and Fayet-Iliopoulos term in analogy to the undeformed case.1 The QS-deformed U(1) theory was independently considered in [15]. 2 A toy model of QS-deformed self-interacting hypermultiplets, with the interaction vanishing in the undeformed limit, was recently considered in [20].3 Nilpotent Q-deformations of the on-shell superfield constraints of the Euclidean N =(2, 2) gauge theory were studied in [21].

On renormalizability of non-anticommutativeN=(1, 0) theories with singlet deformation

“…This situation is very similar to the N = (1/2, 0) gauge model studied in [18], where it was shown that the nonanticommutative interaction also generates new terms in the effective action which can be eliminated from the theory by a shift of the gaugino field. Third, we demonstrate that the appropriate change of fields in the classical actions (a Seiberg-Witten-like map) [6,7] allows one to completely avoid any divergence in the effective action. This fact emphasizes that the divergencies are unphysical from the standard point of view.…”

“…The simplest case C αβ ij = 2Iε αβ ε ij is called the singlet deformation [3,4]. The N = (1, 1) classical models with singlet non-anticommutative deformation have been constructed in [6,7,8]. Note that the singlet non-anticommutative deformations of N = (1, 1) superspace also emerge from string theory considered on the axionic background [6].…”

“…The classical superfield actions for non-anticommutative N = (1, 1) models of the vector multiplet and the hypermultiplet were constructed in harmonic superspace in [3]. The component structure of these actions was studied extensively [6,7,8]. However, the quantum aspects of such models have never been studied.…”

Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model

“…The constant I here is a parameter of non-anticommutativity, Q i α are the supercharges. In particular, the non-anticommutative generalization of the action (2.1) is given by [13] …”

Non-singlet Q-deformed N=(1,0) and N=(1Castro1, Quevedo2 2006Physics Letters B8000View full textAdd to dashboardCite

“…Only for particular purely non-singlet parameters we are able to enhance the supersymmetry to [17,18]. For example, from…”