Supergravity Fluxes and Generalised Geometry

Abstract

We briefly review the description of the internal sector of supergravity theories in the language of generalised geometry and how this gives rise to a description of supersymmetric backgrounds as integrable geometric structures. We then review recent work, featuring holomorphic Courant algebroids, on the description of N=1 heterotic flux vacua. This work studied the finite deformation problem of the Hull–Strominger system, guided by consideration of the superpotential functional on the relevant space of geometries. It rewrote the system in terms of the Maurer–Cartan set of a particular L∞‐algebra associated to a holomorphic Courant algebroid, with the superpotential itself becoming an analogue of a holomorphic Chern–Simons functional.

Hitchhiker's Guide to Courant Algebroid Relations

“…Their relevance was recognized already in the founding paper [1] and the famous letters [2]. Courant algebroids can be used to describe current algebras of σ-models [3], various aspects of T-duality [4,5,6,7], geometrical approach to (exceptional, heterotic) supergravity [8,9,10,11] and Poisson-Lie T-duality [12,13,14,15]. See also recent attempts to describe global geometry of double field theory using para-Hermitian manifolds [16,17,18,19], and our contributions to the subject 1 .…”