Bf Theory on a Brane

An alternative approach to introducing gravitational dynamics on a brane embedded in a higher dimensional spacetime is presented. The brane is treated as a boundary of a higher dimensional manifold in which the bulk action is described by a metric independent topological quantum field theory. The example of a five dimensional non-Abelian BF theory with a boundary brane is considered. A natural boundary condition is adopted chosen for consistency of the topological action despite the presence of a boundary. The resulting effective action on the brane is the action of general relativity in first order form plus terms involving the extrinsic curvature of the brane.