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.

28 pages

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• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
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Cited by in corpus (12)

• Multiple Membranes in M-theory
• Anomalous Dimensions in Non-Supersymmetric Bifundamental Chern-Simons Theories
• Yang-Mills as massive Chern-Simons theory: a third way to three-dimensional gauge theories
• Critical solutions in topologically gauged N=8 CFTs in three dimensions
• The Third Way to Interacting $p$-form Theories
• On-shell versus Off-shell Equivalence in 3D Gravity
• The Third way to 3D Supersymmetric Massive Yang-Mills Theory
• A Review of Third Way Consistent Theories
• Partially Supersymmetric ABJM Theory with Flux
• Quantum and Thermal Fluctuations and Pair-breaking in Planar QED
• Complex Chern-Simons and Gribov
• Wald type analysis for spin-one fields in three dimensions