Eleven-Dimensional Supergravity in 4D, $N=1$ Superspace

TL;DR

This paper develops a linearized 11D supergravity formulation within 4D, N=1 superspace, incorporating all eleven bosonic coordinates and embedding 11D fields into superfield representations consistent with superconformal symmetry.

Contribution

It introduces a novel superspace formulation of 11D supergravity that includes a tensor hierarchy and Kaluza-Klein vectors, extending previous lower-dimensional models.

Findings

Full linearized 11D supergravity action recovered from superspace projection

Superfield representations encode 11D fields within 4D, N=1 superconformal algebra

Tensor hierarchy and gauged diffeomorphisms on the internal manifold are incorporated

Abstract

We give a formulation of linearized 11D supergravity in 4D, $N=1$ superspace keeping all eleven bosonic coordinates. The fields are fluctuations around $\mathbf M=\mathbf R^{4|4}\times Y$, 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.