Twisted Courant algebroids and coisotropic Cartan geometries

In this paper, we show that associated to any coisotropic Cartan geometry there is a twisted Courant algebroid. This includes, in particular, parabolic geometries. By using this twisted Courant algebroid, we give some new results about the Cartan curvature and the Weyl structure of a parabolic geometry. As more direct applications, we can construct a Lie 2-algebra and a three-dimensional (3D) AKSZ sigma model from a coisotropic Cartan geometry.