On conformal supergravity and projective superspace

Abstract

The projective superspace formulation for four-dimensional N = 2 mattercoupled supergravity presented in arXiv:0805.4683 makes use of the variant superspace realization for the N = 2 Weyl multiplet in which the structure group is SL(2, C) × SU(2) and the super-Weyl transformations are generated by a covariantly chiral parameter. An extension to Howe's realization of N = 2 conformal supergravity in which the tangent space group is SL(2, C) × U(2) and the super-Weyl transformations are generated by a real unconstrained parameter was briefly sketched. Here we give the explicit details of the extension.

Non-conformal supercurrents in six dimensions

“…The terminology "O(n) multiplet" was coined in [35]. As 6D N = (1, 0) superconformal multiplets, their complete description was given in [36] following the earlier approaches in four and five dimensions [37][38][39][40].…”

“…Originally it was introduced in four and three dimensions [33,35,58,59] and then extended to five [60] and six [45,61,62] dimensions. The projective-superspace approach to conformal supergravity was first developed in five dimensions [39,63] and then extended to four [40,64,65] and six dimensions [36].…”

Goldstino superfields in N = 2 $$ \mathcal{N}=2 $$ supergravity

“…The three formulations prove to be equivalent, and they are also related to each other in the following sense: (i) SU(2) superspace is a gauged fixed version of U(2) superspace [59]; and (ii) U(2) superspace is a gauge fixed version of conformal superspace [33]. The most general off-shell N = 2 supergravity-matter couplings were constructed in SU(2) superspace [53,54], a few years before the conformal superspace was introduced.…”

“…The most general off-shell N = 2 supergravity-matter couplings were constructed in SU(2) superspace [53,54], a few years before the conformal superspace was introduced. They can uniquely be lifted to U(2) superspace [59] and also to conformal superspace [60]. For certain applications, SU(2) superspace is the simplest formalism to deal with.…”

Supersymmetric Sigma Model Geometry

“…Over the years it has been developed and refined in, e.g., [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In this article we report on some of that development along with some more recent development, such as projective superspace for supergravity [20][21][22][23][24][25], and applications such as the construction of certain classes of hyperkähler metrics [26][27][28].…”