Twisted Courant algebroids and coisotropic Cartan geometries

TL;DR

This paper establishes a connection between coisotropic Cartan geometries and twisted Courant algebroids, leading to new insights into curvature, Weyl structures, and applications in Lie 2-algebras and sigma models.

Contribution

It introduces a novel twisted Courant algebroid framework for coisotropic Cartan geometries, including parabolic geometries, and explores their implications.

Findings

New twisted Courant algebroid structures for coisotropic Cartan geometries

Enhanced understanding of Cartan curvature and Weyl structures

Applications to Lie 2-algebras and 3D AKSZ sigma models

Abstract

In this paper, we show that associated to any coisotropic Cartan geometry there is a twisted Courant algebroid. This includes in particular parabolic geometries. Using this twisted Courant structure, we give some new results about the Cartan curvature and the Weyl structure of a parabolic geometry. As more direct applications, we have Lie 2-algebra and 3D AKSZ sigma model with background associated to any coisotropic Cartan geometry.