6D supersymmetric nonlinear sigma-models in 4D, Script N = 1 superspace

Abstract

Using 4D, N = 1 superfield techniques, a discussion of the 6D sigmamodel possessing simple supersymmetry is given. Two such approaches are described. Foremost it is shown that the simplest and most transparent description arises by use of a doublet of chiral scalar superfields for each 6D hypermultiplet. A second description that is most directly related to projective superspace is also presented. The latter necessarily implies the use of one chiral superfield and one nonminimal scalar superfield for each 6D hypermultiplet. A separate study of models of this class, outside the context of projective superspace, is also undertaken.

Hyperkähler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace

“…The results obtained in the present paper admit a natural extension to 5D [14] and 6D [26,27] projective superspace formulations.…”

Adinkra ‘color’ confinement in exemplary off-shell constructions of 4D, N $$ \mathcal{N} $$ = 2 supersymmetry representations

“…A standard approach to embedding Dirac particles into 4D, N = 1 models is to use a pair of chiral superfields that may be denoted by Φ + and Φ − corresponding to a χ o = 2 system. In a number of our past works [28,[31][32][33], and [34][35][36][37][38], it has been advocated that an alternate approach to embedding Dirac particles into 4D, N = 1 models is to use a 'CMN pair' consisting of one chiral superfield Φ and one complex linear superfield Σ corresponding to a χ o = 0 system. One of the amusing analogies to note is that with respect to off-shell 4D, N = 2 supersymmetry, the adinkra quantum number χ o defined on 4D, N = 1 supermultiplets acts just like color in hadronic physics!…”

Partial $$ \mathcal{N} $$ = 2 supersymmetry breaking and deformed hypermultiplets

“…It would be interesting to modify our setup to allow for more general central extensions of the N = 2 Poincaré algebra. In particular, this naturally leads to the study of 5D and 6D models in terms of 4D superfields as for instance in [66][67][68].…”

“…One method to do this is with the use of projective superspace [30][31][32][33]; see [37,38] for reviews. In the case of projective superspace with central charge and unbroken 4D N = 2 supersymmetry the reader might look at the JHEP03(2019)037 following papers [64,65] and, in the related cases of a 4D description with central charges of 5D and 6D multiplets, the papers [66][67][68]. 9 It is convenient to first break the SU(2) covariant notation of the N = 2 superspace derivatives by defining…”