M-theory, exceptional generalised geometry and superpotentials

Understand

We discuss the structure of "exceptional generalised geometry" (EGG), an extension of Hitchin's generalised geometry that provides a unified geometrical description of backgrounds in eleven-dimensional supergravity.

• On a d-dimensional background, as first described by Hull, the action of the generalised geometrical O(d,d) symmetry group is replaced in EGG by the exceptional U-duality group E_d(d).
• The metric and form-field degrees of freedom combine into a single geometrical object, so that EGG naturally describes generic backgrounds with flux, and there is an EGG analogue of the Courant bracket which encodes the differential geometry.
• Our focus is on the case of seven-dimensional backgrounds with N=1 four-dimensional supersymmetry.