  We discuss the Josephson effect and the appearance of dissipationless edge
currents in a holographic Josephson junction configuration involving a chiral,
time-reversal breaking, superconductor in 2+1 dimensions. Such a superconductor
is expected to be topological, thereby supporting topologically protected
gapless Majorana-Weyl edge modes. Such modes manifest themselves in chiral
dissipationless edge currents, which we exhibit and investigate in the context
of our construction. The physics of the Josephson current itself, though
expected to be unconventional in some non-equilibrium settings, is shown to be
conventional in our setup which takes place in thermal equilibrium. We comment
on various ways in which the expected Majorana nature of the edge excitations,
and relatedly the unconventional nature of topological Josephson junctions, can
be verified in the holographic context.
