Born Geometry in a Nutshell

TL;DR

This paper summarizes para-Hermitian and Born geometries that underpin T-duality in string theory, introducing a generalized framework for describing doubled target spaces and their physical spacetime recovery.

Contribution

It provides a concise overview of Born geometry, including the generalized structures, connections, and fluxes relevant for string theory backgrounds.

Findings

Introduces a generalized differentiable structure on doubled spaces.

Defines the Born connection as a generalization of Levi-Civita connection.

Discusses flux-induced twisting of the geometric structures.

Abstract

We give a concise summary of the para-Hermitian geometry that describes a doubled target space fit for a covariant description of T-duality in string theory. This provides a generalized differentiable structure on the doubled space and leads to a kinematical setup which allows for the recovery of the physical spacetime. The picture can be enhanced to a Born geometry by including dynamical structures such as a generalized metric and fluxes which are related to the physical background fields in string theory. We then discuss a generalization of the Levi-Civita connection in this setting - the Born connection - and twisting of the kinematical structure in the presence of fluxes.