  The excitation spectrum of a two-dimensional $p_x+ip_y$ fermionic superfluid,
such as a thin film of $^3$He-A, includes a gapless Majorana-Weyl fermion which
is confined to the boundary by Andreev reflection. There is also a persistent
ground-state boundary current which provides a droplet containing $N$ particles
with angular momentum $\hbar N/2$. Both of these boundary effects are
associated with bulk Chern-Simons effective actions. We show that the gapless
edge-mode is required for the gauge invariance of the total effective action,
but the same is not true of the boundary current.
