Abstract
Motivated by recent efforts to encode 11D supergravity in 4D mathcal{N} = 1 superfields, we introduce a general covariant framework relevant for describing any higher dimensional supergravity theory in external 4D mathcal{N} = 1 superspace with n additional internal coordinates. The superspace geometry admits both external and internal diffeomorphisms and provides the superfields necessary to encode the components of the higher dimensional vielbein, except for the purely internal sector, in a universal way that depends only on the internal dimension n. In contrast, the mathcal{N} = 1 superfield content of the internal sector of the metric is expected to be highly case dependent and involve covariant matter superfields, with additional hidden higher dimensional Lorentz and supersymmetry transformations realized in a non-linear manner.
Highlights
Introduction and motivationA major difficulty in studying higher-dimensional supergravity theories is the absence of a off-shell formulation
This introduces anew the old problem of solving superspace Bianchi identities, but with the added wrinkle of an additional set of coordinates and a slew of new superfields describing the mixed curvatures. It turns out this can be done in a rather universal way, which seems as applicable to minimal 5D supergravity as to 11D supergravity, the details of intermediate cases have not yet been worked out. We provide such a generic reformulation of 4D N = 1 superspace with n additional internal coordinates. (Our interest is n = 7, but the formulae are agnostic to the specific choice.) Our construction will be motivated by the requirement that it consistently covariantize the 11D supergravity results
The goal of this paper has been to construct a general framework in 4D N = 1 superspace that is suitable for describing a higher-dimensional supergravity theory in 4+ n dimensions
Summary
A major difficulty in studying higher-dimensional supergravity theories is the absence of a (finite) off-shell formulation. The explanation offered in [17] was that the gravitino superfield, which encodes the additional seven gravitini, should include auxiliary vector and tensor fields that when integrated out modify the kinetic terms in the 7 This was demonstrated to be the case in [18] where the entire linearized action was written down in N = 1 superspace. The N = 1 gravitino combines with the external graviton into a single supermultiplet, described by a prepotential superfield Hαα = (σa)αα Ha, subject to a linearized gauge transformation δHαα = DαLα − Dα ̇ Lα. If we ignore the Ω parameter in the linearized transformation (2.9), it is possible to combine the linearized Hααand Ψmα into an abelian tensor hierarchy, just like the 3-form fields, where the Kaluza-Klein gauge field appears encoded in the covariant derivatives. We will argue in the conclusion that this is so
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