N=1 Supercurrents of Eleven-dimensional Supergravity

TL;DR

This paper develops a superspace formulation of eleven-dimensional supergravity on manifolds with a G2-structure, deriving a comprehensive action that captures the supergravity dynamics and their geometric origins.

Contribution

It constructs the full nonlinear superspace action for eleven-dimensional supergravity with G2-structure, extending previous linear approximations and linking geometric data to supersymmetric field theories.

Findings

Derived the all-order $O()$ superspace action in fields

Connected the supergravity structure to G2-geometry and Hitchin functional

Provided a parameterization via complex spinors encoding off-shell algebra

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.