# Hitchhiker’s guide to Courant algebroid relations

@article{Vysok2020HitchhikersGT, title={Hitchhiker’s guide to Courant algebroid relations}, author={Jan Vysok{\'y}}, journal={Journal of Geometry and Physics}, year={2020}, volume={151}, pages={103635} }

Abstract Courant algebroids provide a useful mathematical tool (not only) in string theory. It is thus important to define and examine their morphisms. To some extent, this was done before using an analogue of canonical relations known from symplectic geometry. However, it turns out that applications in physics require a more general notion. We aim to provide a self-contained and detailed treatment of Courant algebroid relations and morphisms. A particular emphasis is placed on providing enough…

## 2 Citations

Born sigma-models for para-Hermitian manifolds and generalized T-duality

- Physics, Mathematics
- 2019

We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized…

Odd transgression for Courant algebroids

- Mathematics
- 2021

Abstract The “odd transgression” introduced in Bressler and Rengifo (2018) is applied to construct and study the inverse image functor in the theory of Courant algebroids.

## References

SHOWING 1-10 OF 70 REFERENCES

Courant Algebroid Connections and String Effective Actions

- Mathematics, Physics
- 2016

Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant…

Courant Algebroids, Poisson–Lie T-Duality, and Type II Supergravities

- Mathematics, Physics
- 2018

We reexamine the notions of generalized Ricci tensor and scalar curvature on a general Courant algebroid, reformulate them using objects natural w.r.t. pull-backs and reductions, and obtain them from…

Courant algebroids, derived brackets and even symplectic supermanifolds

- Mathematics
- 1999

In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant…

Courant Algebroids

- Physics, Mathematics
- 2005

This paper is devoted to studying some properties of the Courant algebroids: we explain the so-called"conducting bundle construction"and use it to attach the Courant algebroid to Dixmier-Douady gerbe…

Transitive Courant Algebroids, String Structures and T-duality

- Mathematics, Physics
- 2013

In this paper, we use reduction by extended actions to give a construction of transitive Courant algebroids from string classes. We prove that T-duality commutes with the reductions and thereby…

Courant Algebroids and Poisson Geometry

- Mathematics
- 2009

Given a manifold M with an action of a quadratic Lie algebra , such that all stabilizer algebras are coisotropic in , we show that the product becomes a Courant algebroid over M. If the bilinear form…

Courant morphisms and moment maps

- Mathematics
- 2008

We study Hamiltonian spaces associated with pairs (E,A), where E is a Courant algebroid and A\subset E is a Dirac structure. These spaces are defined in terms of morphisms of Courant algebroids with…

Ricci flow, Killing spinors, and T-duality in generalized geometry

- Mathematics, PhysicsAdvances in Mathematics
- 2019

We introduce a notion of Ricci flow in generalized geometry, extending a previous definition by Gualtieri on exact Courant algebroids. Special stationary points of the flow are given by solutions to…

On the structure of graded symplectic supermanifolds and Courant algebroids

- Mathematics, Physics
- 2002

This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles…

Algebroid structures on para-Hermitian manifolds

- Mathematics, PhysicsJournal of Mathematical Physics
- 2018

We present a global construction of a so-called D-bracket appearing in the physics literature of Double Field Theory (DFT) and show that if certain integrability criteria are satisfied, it can be…