Generalized geometry applied to 4d-supergravity

TL;DR

This paper explores the application of generalized complex geometry to a simplified model of eleven-dimensional M-theory, aiming to unify geometric structures relevant to string theory and supergravity.

Contribution

It develops a formalism based on generalized geometry concepts for three-form supergravity, extending ideas from string theory to M-theory models.

Findings

Unified symplectic and complex structures in M-theory context

Formalism for three-form supergravity using generalized geometry

Potential insights into T-duality and M-theory geometry

Abstract

Generalized complex geometry is an example of a powerful formalism to attempt the construction of a language adequate to string theory. With the remarkable property of unifying symplectic and complex manifolds as special cases of a broader structure it is proving to be the right tool to use when trying to describe T-duality. The key idea was to look at both geometries as operations in the direct sum of tangent and cotangent bundle as opposed to the usual approach, where only the tangent spaces are relevant. In this thesis we will be interested in developing a formalism drinking from these ideas but for a toy model of eleven dimensional M-theory: three-form supergravity as introduced by Ovrut and Waldram.