Unravelling the novel Higgs mechanism in (2+1)d Chern-Simons theories

Abstract

Chern-Simons gauge theories in 2+1 dimensions with multiple gauge fields exhibit novel properties that are analysed here in some detail. A striking feature is the possibility of a non-propagating Chern-Simons field acquiring a massless propagating mode via a Higgs mechanism. This novel Higgs mechanism, originally discovered in the context of M-theory, is studied here without reference to M-theory or supersymmetry. It is revealed as a variant of topological mass generation and shown to arise only when Chern-Simons and mass matrices are not simultaneously diagonalisable. Sufficient conditions are found for it to occur. It is speculated that some analogue of the NHM could occur in theories of condensed-matter systems similar to those exhibiting the fractional quantum Hall effect, as well as in 2+1 dimensional gravity.