The E_{11} origin of all maximal supergravities

TL;DR

This work shows that maximal supergravities in dimensions $D\ge 3$ (including massive, gauged cases) originate from the eleven-dimensional $E_{11}$ non-linear realisation of M-theory. By decomposing the $E_{11}$ adjoint and performing dimensional reductions, the authors classify all propagating forms, as well as $D-1$ and $D$-forms, and demonstrate that $D-1$ forms encode the full set of mass deformations while $D$-forms correspond to spacetime-filling branes, in line with string/M-theory orientifolds. The dynamics of gauged supergravities are shown to arise from the same $E_{11}$ structure via embedding-tensor data and a covariant Maurer–Cartan construction, with explicit matching across dimensions and well-known examples such as Romans IIA, $SO(8)$ in $D=4$, and $SO(6)$ in $D=5$. Overall, the results strongly support an eleven-dimensional origin and physical role for many $E_{11}$ adjoint fields, suggesting that $E_{11}$ is a fundamental symmetry of low-energy M-theory and its compactifications.

Abstract

Starting from the eleven dimensional E_{11} non-linear realisation of M-theory we compute all possible forms, that is objects with totally antisymmetrised indices, that occur in four dimensions and above as well as all the 1-forms and 2-forms in three dimensions. In any dimension D, the D-1-forms lead to maximal supergravity theories with cosmological constants and they are in precise agreement with the patterns of gauging found in any dimension using supersymmetry. The D-forms correspond to the presence of space-filling branes which are crucial for the consistency of orientifold models and have not been derived from an alternative approach, with the exception of the 10-dimensional case. It follows that the gaugings of supergravities and the spacetime-filling branes possess an eleven dimensional origin within the E_{11} formulation of M-theory. This and previous results very strongly suggest that all the fields in the adjoint representation of E_{11} have a physical interpretation.

Figures (10)

• Figure 1: The $E_{11}$ Dynkin diagram corresponding to 11-dimensional supergravity.
• Figure 2: The $E_{11}$ Dynkin diagram corresponding to 10-dimensional IIA supergravity.
• Figure 3: The $E_{11}$ Dynkin diagram corresponding to 10-dimensional IIB supergravity. The internal symmetry group is $SL(2,\mathbb{R})$.
• Figure 4: The $E_{11}$ Dynkin diagram corresponding to 9-dimensional supergravity. The non-abelian part of the internal symmetry group is $SL(2,\mathbb{R})$.
• Figure 5: The $E_{11}$ Dynkin diagram corresponding to 8-dimensional supergravity. The internal symmetry group is $SL(3,\mathbb{R}) \times SL(2,\mathbb{R})$.