Eleven-dimensional supergravity in 4D, N = 1 superspace

Abstract

Abstract:We give a formulation of linearized 11D supergravity in 4D, N = 1 superspace keeping all eleven bosonic coordinates. The fields are fluctuations around M = R 4|4 × Y , where Y is a background Riemannian 7-manifold admitting a G 2 structure. We embed the 11D fields into superfield representations of the 4D, N = 1 superconformal algebra. These consist of the conformal graviton superfield, seven conformal gravitino superfields, a tensor hierarchy of superfields describing the 11D 3-form, and a non-abelian Kaluza-Klein vector multiplet gauging the tensor hierarchy by diffeomorphisms on Y . The quadratic action consists of the linearization of a superspace volume term and a Chern-Simons action for the gauged hierarchy coupled to the supergravity and gravitino superfields, and the full structure is fixed by superconformal and gauge invariance. When this action is projected to components, we recover the full linearized action of 11D supergravity.

Abelian tensor hierarchy in 4D, N = 1 superspace

“…On the other hand, the remaining supergravity components have not yet been accounted for and it is known from previous work [25,26] that including these superspin-3 2 and -1 multiplets has the potential to resolve this mismatch. Including the coupling to these fields is work currently in progress [20]. The goal ultimately is to the embed the action eq.…”

“…In a forthcoming publication this is generalized to a non-Abelian tensor hierarchy by gauging [19]. The construction of the locally supersymmetric generalization is in progress [20].…”

Five-dimensional supergravity in N = 1/2 superspace

“…As discussed in [30], for this to be consistent with y-dependence of the 4D supergraviton, we will be required to incorporate also the gravitino superfield corrections to the supergeometry: The graviton transformation (2.1) must be allowed to depend on y, so we expect terms ∼ ∂ y L α to appear that we need to be able to cancel. This can be done provided we modify the gravitino superfield transformation (2.3) by a term ∼ ∂ y L α [14,29]. 6 This gravitino superfield, in turn, contributes its torsions and curvatures to the covariant derivative algebra [32,37], which would first need to be constructed.…”

“…The ingredients in the first line are as follows: L omsg [G, U a ] is the linearized action of old-minimal supergravity. It can be written in various forms, one of which is [29] L…”

“…Nevertheless, it was explicitly shown that it does work for 10D super-Yang-Mills in [24]. More recently, the approach was extended to the far more subtle case of elevendimensional supergravity in [25][26][27][28][29][30].…”