  The 4D Maxwell theory with single-sided planar boundary is considered. As a
consequence of the presence of the boundary, two broken Ward identities are
recovered, which, on-shell, give rise to two conserved currents living on the
edge. A Ka\c{c}-Moody algebra formed by a subset of the bulk fields is obtained
with central charge proportional to the inverse of the Maxwell coupling
constant, and the degrees of freedom of the boundary theory are identified as
two vector fields, also suggesting that the 3D theory should be a gauge theory.
Finally the holographic contact between bulk and boundary theory is reached in
two inequivalent ways, both leading to a unique 3D action describing a new
gauge theory of two coupled vector fields with a topological Chern-Simons term
with massive coefficient. In order to check that the 3D projection of 4D
Maxwell theory is well defined, we computed the energy-momentum tensor and the
propagators. The role of discrete symmetries is briefly discussed.
