Generalized Geometry and M theory

TL;DR

This paper reformulates eleven-dimensional supergravity using generalized geometry, unifying the metric and three-form, and making duality symmetries explicit without dimensional reduction.

Contribution

It introduces a new formulation of supergravity that unifies key fields via generalized geometry, highlighting duality symmetries in eleven dimensions.

Findings

Manifest duality group in four spatial dimensions.

Unified description of metric and C-field without dimensional reduction.

Detailed relationship between twisted Courant algebra and gauge symmetries.

Abstract

We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and C-field are on an equal footing even though no dimensional reduction is required for our results to hold. One may also describe our results using the generalized geometry that emerges from membrane duality. The relationship between the twisted Courant algebra and the gauge symmetries of eleven dimensional supergravity are described in detail.