N=1 Supercurrents of Eleven-dimensional Supergravity

Abstract

Eleven-dimensional supergravity can be formulated in superspaces locally of the form $\mathbf{X}\times Y$ where $\mathbf{X}$ is 4D $N=1$ conformal superspace and $Y$ is an arbitrary 7-manifold admitting a $G_2$-structure. The eleven-dimensional 3-form and the stable 3-form on $Y$ define the lowest component of a gauge superfield on $\mathbf{X}\times Y$ that is chiral as a superfield on $\mathbf{X}$. This chiral field is part of a tensor hierarchy giving rise to a superspace Chern-Simons action and its real field strength defines a lifting of the Hitchin functional on $Y$ to the $G_2$ superspace $\mathbf{X}\times Y$. These terms are those of lowest order in a superspace Noether expansion in seven $N=1$ conformal gravitino superfields $\Psi$. In this paper, we compute the $O(\Psi )$ action to all orders in the remaining fields. The eleven-dimensional origin of the resulting non-linear structures is parameterized by the choice of a complex spinor on $Y$ encoding the off-shell 4D $N=1$ subalgebra of the eleven-dimensional super-Poincare algebra.

References in corpus (6)

• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Abelian Tensor Hierarchy in 4D, N=1 Superspace
• Eleven-Dimensional Supergravity in 4D, $N=1$ Superspace
• Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace
• M-theory Potential from the $G_2$ Hitchin Functional in Superspace
• All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies

Cited by in corpus (6)

• Maximally twisted eleven-dimensional supergravity
• Five-dimensional Supergravity in N = 1/2 Superspace
• Components of Eleven-dimensional Supergravity with Four Off-shell Supersymmetries
• 4D N=1 Kaluza-Klein superspace
• Weyl Covariance, and Proposals for Superconformal Prepotentials in 10D Superspaces
• Linearized Off-shell 4+7 Supergeometry of 11D Supergravity