Metric bundles of split signature and type II supergravity

Abstract

We study the geometry of type II supergravity compactifications in terms of an oriented vector bundle E, endowed with a bundle metric of split signature and further datum. The geometric structure is associated with a so-called generalised G-structure and characterised by an E-spinor ρ, which we can regard as a differential form of mixed degree. This enables us to reformulate the field equations of type II supergravity as an integrability condition of type dH ρ = 0, where dH = d + H∧ is the twisted differential on forms. Finally, we investigate some geometric properties of integrable structures and formulate various no-go theorems.