Abstract
Abstract In this short paper, we will review the proposal of a correspondence between the doubled geometry of Double Field Theory and the higher geometry of bundle gerbes. Double Field Theory is T-duality covariant formulation of the supergravity limit of String Theory, which generalises Kaluza-Klein theory by unifying metric and Kalb-Ramond field on a doubled-dimensional space. In light of the proposed correspondence, this doubled geometry is interpreted as an atlas description of the higher geometry of bundle gerbes. In this sense, Double Field Theory can be interpreted as a field theory living on the total space of the bundle gerbe, just like Kaluza-Klein theory is set on the total space of a principal bundle. This correspondence provides a higher geometric interpretation for para-Hermitian geometry which opens the door to its generalisation to Exceptional Field Theory. This review is based on, but not limited to, my talk at the workshop Generalized Geometry and Applications at Universität Hamburg on 3rd of March 2020.
Highlights
One of the most characteristic and fascinating features of String Theory, when compared to the usual eld theories, is the appearance of T-duality: an additional, hidden symmetry of the theory
In this short paper, we will review the proposal of a correspondence between the doubled geometry of Double Field Theory and the higher geometry of bundle gerbes
Double Field Theory can be interpreted as a eld theory living on the total space of the bundle gerbe, just like Kaluza-Klein theory is set on the total space of a principal bundle
Summary
One of the most characteristic and fascinating features of String Theory, when compared to the usual eld theories, is the appearance of T-duality: an additional, hidden symmetry of the theory. On one side of the correspondence, the Lie -algebra string = Rd ⊕ bu( ) is the linearisation of a bundle gerbe and, on the other side, the para-Kähler vector space Rd ⊕ (Rd)*, J, ω is the linearisation of a para-Hermitian manifold. Rd ⊕ (Rd)*, J, ω bundle gerbe para-Hermitian manifold (i.e. doubled space)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
