Generalised Geometries and Lie Algebroid Gauging

Abstract

This thesis investigates the role of algebroid geometries in string theory. Differential geometry provides the framework for general relativity and point particle dynamics. The dynamics of strings and higher dimensional branes are most naturally described by algebroid geometry on vector bundles---with fluxes being incorporated as geometric data describing twisted vector bundles. This thesis contains original results in two areas: Firstly, twisted generalised contact structures and generalised coKahler structures are studied. Secondly, a non-isometric gauging proposal based on Lie algebroids is studied from a geometric perspective. We study generalised contact structures from the point of view of reduced generalised complex structures; naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail with a geometric description given in terms of gerbes. As an application of the reduction procedure we define generalised coKahler structures in a way which extends the Kahler/coKahler correspondence.

An invariant geometric approach to the Lie algebroid gauging proposal of Kotov and Strobl [114,99,89,90] is presented. The existing literature on Lie algebroid gauging is purely local. We consider global aspects through the integrability of a local algebroid action. The main result is that it is always possible to provide a local non-isometric gauging for any arbitrary background. The necessary and sufficient conditions to gauge with respect to a given choice of vector fields are given. However, requiring a gauge invariant field strength term restricts to Lie groupoids that are locally isomorphic to Lie groups. As an application of this work the proposal of Chatzistavrakidis, Deser, and Jonke for "T-duality without isometry" is studied. We show that this non-isometric T-duality proposal is in fact equivalent to non-abelian T-duality by an appropriate field redefinition. Show more