The geometry behind double geometry

Understand

Generalised diffeomorphisms in double field theory rely on an O(d,d) structure defined on tangent space.

• We show that any (pseudo-)Riemannian metric on the doubled space defines such a structure, in the sense that the generalised diffeomorphisms defined using such a metric form an algebra, provided a covariant section condition is fulfilled.
• Consistent solutions of the section condition gives further restrictions.
• The case previously considered corresponds to a flat metric.