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

TL;DR

This paper explores a novel Higgs mechanism in 2+1 dimensional Chern-Simons gauge theories where non-propagating fields gain massless modes, revealing new mass generation phenomena beyond traditional models.

Contribution

It demonstrates the existence of a unique Higgs mechanism in Chern-Simons theories that does not rely on supersymmetry or M-theory, expanding understanding of topological mass generation.

Findings

Identifies conditions for the novel Higgs mechanism to occur.

Shows that the mechanism arises when Chern-Simons and mass matrices are not diagonalisable.

Suggests potential applications in condensed matter and gravity 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.