  The current algebra generated by fermions coupled to external gauge
potentials and metrics on a manifold with boundary is discussed. It is shown
that the previous methods, based on index theory arguments and used in the case
without boundaries, carry over to the present problem. The resulting current
algebra is the same as obtained from a quantization of bosonic Chern-Simons
theories on space-times with nonempty boundaries. This means that also in the
fermionic setting the construction is 'holographic', the Schwinger terms reside
on the boundary.
