We review recently introduced geometric tools used to characterize supersymmetric flux backgrounds, with special emphasis on Generalised Complex Geometry as developed by Hitchin. We then proceed to describe Exceptional Generalised Geometry, an extension of the latter formalism
based on the exceptional Lie group $E_7(7)$ which achieves a full geometrization of all fluxes, including Ramond-Ramond fluxes. First we present the formal structure of the theory: the Exceptional Generalized Tangent bundle endowed with a non-trivial twisted topology and a corresponding gerbe structure, an Exceptional Courant bracket and an Exceptional Generalized Metric in which the bosonic degrees of freedom of 11D supergravity (the traditional metric and the fluxes) enter on equal
footing. We then show how this formalism may be used to rewrite part of 11D SUGRA in the language of N=1 D=4 supersymmetry and express the corresponding effective superpotential in a manifestly $E_7(7)$ form. |