Non-Abelian bosonization and topological aspects of BCS systems

Abstract

It is shown that many features of the low energy behaviour of weak coupling BCS systems are topological in character. This is done by writing the BCS action as a Fermi surface sum of (1 + 1)-dimentional non-Abelian actions, each one of which can be bosonized à la Witten. This process leads to the correct current generating parts (as found by Cross) in the effective action for the gap function, and in addition a Wess-Zumino term. The mass and spin currents are calculated for the three-dimensional theory, and it is shown that upon averaging over all directions on the Fermi surface, the contribution from the Wess-Zumino term vanishes for a pure spin singlet or pure spin triplet gap, but not otherwise.