Boundary Terms in Generalized Geometry and doubled field theory

We propose a boundary action to complement the recently developed duality manifest actions in string and M-theory using generalized geometry. This boundary action combines the Gibbons-Hawking term with boundary pieces that were previously neglected in the construction of these actions. The combination may be written in terms of the metric of generalized geometry. The result is to produce an action that is duality invariant including boundary terms.