Generalized Geometry and M theory

TL;DR

This work reformulates the bosonic sector of eleven-dimensional supergravity in a generalized geometric framework that unifies the spacetime metric and the 3-form into a single SL(5) structure, without any dimensional reduction. Through a Hamiltonian treatment and membrane duality, it introduces a generalized metric M_{MN} acting on an extended space with coordinates (x^a,y_{ab}) and demonstrates that the dynamics can be written as T+V with a manifest SL(5) invariance, reproducing the familiar R(oldsymbol{ abla}) and F^2 terms when restricted to the physical section. The analysis connects the gauge symmetries, Courant-type algebras, and M-theory dualities, and presents a coherent route to higher duality groups (e.g., E_8) and non-geometric backgrounds. While the construction is currently realized in the purely bosonic sector and under a section condition, it offers a principled framework for duality-invariant formulations of M-theory and points to future work on curvature notions, time-like dualities, and fermionic sectors.

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.