Double Field Theory and Geometric Quantisation

TL;DR

This paper explores the geometric quantisation of double field theory and the doubled string sigma model, focusing on T-duality as a symplectic transformation and introducing a double coherent state for duality frames.

Contribution

It applies geometric quantisation techniques to double field theory, offering new insights into T-duality and constructing a stringy deformed Fourier transform.

Findings

T-duality as symplectic transformation in quantisation

Construction of double coherent states

Development of a stringy deformed Fourier transform

Abstract

We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of polarisation in the construction of the quantum bundle for the string. Following this perspective we adopt a variety of techniques from geometric quantisation to study the doubled space. One application is the construction of the double coherent state that provides the shortest distance in any duality frame and a stringy deformed Fourier transform.