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 Kaç–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.