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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 whichis confined to the boundary by Andreev reflection. There is also a persistentground-state boundary current which provides a droplet containing $N$ particleswith angular momentum $\hbar N/2$. Both of these boundary effects areassociated with bulk Chern-Simons effective actions. We show that the gaplessedge-mode is required for the gauge invariance of the total effective action,but the same is not true of the boundary current.Comment: 16 pages. Uses Revtex

physical review. b, condensed matter and materials physics

Edge modes, edge currents, and gauge invariance in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superfluids and superconductors

Edge modes, edge currents, and gauge invariance inpx+ipysuperfluids and superconductors