  We study a topological field theory in four dimensions on a manifold with
boundary. A bulk-boundary interaction is introduced through a novel variational
principle rather than explicitly. Through this scheme we find that the boundary
values of the bulk fields act as external sources for the boundary theory.
Furthermore, the full quantum states of the theory factorize into a single bulk
state and an infinite number of boundary states labeled by loops on the spatial
boundary. In this sense the theory is purely holographic. We show that this
theory is dual to Chern-Simons theory with an external source. We also point
out that the holographic hypothesis must be supplemented by additional
assumptions in order to take into account bulk topological degrees freedom,
since these are apriori invisible to local boundary fields.
