Generalised Cartan Geometry

TL;DR

This paper introduces a Cartan-geometric framework for generalized geometries using differential graded Lie algebras, extending tangent bundles and incorporating duality and gauge groups, with applications to M-theory branes.

Contribution

It systematically constructs generalized connections, torsion, and curvature tensors within a novel Cartan-geometric approach for broad classes of geometries.

Findings

Provides a unified framework for generalized geometries.

Constructs generalized connections, torsion, and curvature tensors.

Applies algebraic structures to M-theory brane phase space.

Abstract

This talk introduces a Cartan-geometric framework for generalised geometries governed by a differential graded Lie algebra. In contrast to ordinary Cartan geometry, the tangent bundle is extended and qu both a global duality group and a local gauge group. This framework provides a systematic construction of generalised connections and their torsion and curvature tensors for generic generalised geometries. We also review the realisation of these algebraic structures on the phase space of branes in M-theory.