# Towards an extended/higher correspondence

@article{Alfonsi2021TowardsAE,
title={Towards an extended/higher correspondence},
author={Luigi Alfonsi},
journal={Complex Manifolds},
year={2021},
volume={8},
pages={302 - 328}
}
• L. Alfonsi
• Published 1 January 2021
• Mathematics
• Complex Manifolds
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…
2 Citations

## Figures from this paper

• Mathematics
Complex Manifolds
• 2021
Abstract We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their
Abstract This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes

## References

SHOWING 1-10 OF 91 REFERENCES

Kaluza‐Klein Theory states that a metric on the total space of a principal bundle P→M , if it is invariant under the principal action of P, naturally reduces to a metric together with a gauge field
In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kahler manifolds. In this paper, we show that the same geometric constructions
The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological
• Physics
• 2014
A bstractA new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric WZW model in the large level limit. This generalizes the
• Mathematics
• 2017
A bstractWe formulate a kinematical extension of Double Field Theory on a 2d-dimensional para-Hermitian manifold Pηω$$\left(\mathcal{P},\eta, \omega \right)$$ where the O(d, d) metric η is
• Mathematics
• 2008
We discuss the structure of "exceptional generalised geometry" (EGG), an extension of Hitchin's generalised geometry that provides a unified geometrical description of backgrounds in
• Mathematics
• 2016
We elaborate on the construction of a prequantum 2-Hilbert space from a bundle gerbe over a 2-plectic manifold, providing the first steps in a programme of higher geometric quantisation of closed
• Mathematics
Journal of High Energy Physics
• 2020
Poisson-Lie duality provides an algebraic extension of conventional Abelian and non-Abelian target space dualities of string theory and has seen recent applications in constructing quantum group
• Mathematics
Fortschritte der Physik
• 2018
We survey physical models which capture the main concepts of double field theory on para‐Hermitian manifolds. We show that the geometric theory of Lagrangian and Hamiltonian dynamical systems is an