Conserved chiral currents on the boundary of 3D Maxwell theory

In this paper the 3D Maxwell theory with single-sided planar boundary is studied. As a consequence of the existence, on the boundary, of two Ward identities, we find two chiral conserved edge currents satisfying a Ka\c{c}-Moody algebra with central charge equal to the inverse of the Maxwell coupling constant. We show that the boundary degrees of freedom are two 2D scalar chiral bosons whose chiralities depend on the parameters of the bulk Maxwell theory. In particular, the edge chiral bosons may have opposite chiralities, in close analogy with the "spinon" and "holon" currents characterizing the 3D topological insulators.