Eleven-Dimensional Supergravity in Light-Cone Superspace

TL;DR

This work presents a compact formulation of eleven-dimensional supergravity in light-cone superspace by oxidizing the ${ m N}=8$, $d=4$ theory into ${ m N}=1$, $d=11$ using a constrained chiral superfield. The authors construct the eleven-dimensional SuperPoincaré algebra, introduce generalized transverse derivatives that transform as an $SO(9)$ vector, and demonstrate the cubic vertex is invariant to order $ appa$; they also conjecture a quartic vertex and develop a chiralization procedure to preserve supersymmetry at higher orders. Central to the approach is the explicit realization of the $SO(9)$ little group and the use of a single superfield to encode all physical degrees of freedom, avoiding auxiliary fields. The framework sets the stage for a detailed analysis of ultraviolet divergences and provides a bridge between ${ m N}=4$ Yang–Mills oxidation and eleven-dimensional supergravity, with potential implications for M-theory.

Abstract

We show that Supergravity in eleven dimensions can be described in terms of a constrained superfield on the light-cone, without the use of auxiliary fields. We build its action to first order in the gravitational coupling constant κ, by "oxidizing" (N=8,d=4) Supergravity. This is simply achieved, as for N=4 Yang-Mills, by extending the transverse derivatives into superspace. The eleven-dimensional SuperPoincare algebra is constructed and a fourth order interaction is conjectured.