Gauged Supergravities, Tensor Hierarchies, and M-Theory

TL;DR

The paper demonstrates that gauged maximal supergravities, formulated via the embedding tensor $\Theta$, inherently require a hierarchy of higher-rank tensor fields, revealing new M-theory degrees of freedom beyond conventional supergravity. By analyzing the complete tensor hierarchy, SUSY algebra, and a Lagrangian that includes all $p$-forms in three dimensions (with $G=E_{8(8)}$), the authors show how the embedding tensor simultaneously selects gauge groups, dictates intertwiners among form fields, and governs duality relations connecting field strengths to $\Theta$. They establish that the $(D-1)$- and $D$-forms encode constancy and closure conditions for the gauging, and that the scalar potential is encoded in a non-positive definite matrix ${\mathbb V}$. This framework yields a universal, non-polynomial Lagrangian that can realize all gaugings, and they discuss connections to infinite-dimensional duality symmetries ($E_{11}$, $E_{10}$) and to M-theory degrees of freedom beyond standard Kaluza–Klein reductions, suggesting a deep, non-perturbative structure underlying M-theory.

Abstract

Deformations of maximal supergravity theories induced by gauging non-abelian subgroups of the duality group reveal the presence of charged M-theory degrees of freedom that are not necessarily contained in supergravity. The relation with M-theory degrees of freedom is confirmed by the representation assignments under the duality group of the gauge charges and the ensuing vector and tensor gauge fields. The underlying hierarchy of these gauge fields is required for consistency of general gaugings. As an example gauged maximal supergravity in three space-time dimensions is presented in a version where all possible tensor fields appear.