Generalised Geometry for M-Theory

TL;DR

This paper extends the framework of generalised geometry to include structures relevant for M-theory and string theory flux backgrounds, introducing new symmetry groups and geometric structures for various p-form fields.

Contribution

It develops a unified geometric framework for M-theory and string theory flux backgrounds using extended symmetry groups and structures.

Findings

Framework for M-theory solutions with flux

Extension to type IIA/IIB string solutions

Discussion of structures for supersymmetric backgrounds

Abstract

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge field on which there is a natural action of the group $E_{d}$. This provides a framework for the discussion of M-theory solutions with flux. A different generalisation is to d-dimensional manifolds with a metric, 2-form gauge field and a set of p-forms for $p$ either odd or even on which there is a natural action of the group $E_{d+1}$. This is useful for type IIA or IIB string solutions with flux. Further generalisations give extended tangent bundles and extended spin bundles relevant for non-geometric backgrounds. Special structures that arise for supersymmetric backgrounds are discussed.