Deriving three-dimensional bosonization and the duality web

Abstract

Recently, a duality web for three dimensional theories with Chern-Simons terms was proposed. This can be derived from a single bosonization type duality, for which various supporting arguments (but not a proof) were given. Here we explicitly derive this bosonization, in the Abelian case and for a particular regime of parameters. To do this, we use the particle-vortex duality in combination with a Buscher-like duality (both considered in the regime of low energies). As a corollary, Son's conjectured duality is derived in a somewhat singular limit of vanishing mass.

10 pages, Latex

References in corpus (8)

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• Baryons, monopoles and dualities in Chern-Simons-matter theories
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• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
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Cited by in corpus (8)

• Conformality loss and quantum criticality in topological Higgs electrodynamics in 2+1 dimensions
• Duality between 3D Massive Thirring and Maxwell Chern-Simons models from 2D bosonization
• One-dimensional bosonization and the SYK model
• Fermion-fermion duality in 3+1 dimensions
• Bosonization in 2+1 dimensions via Chern-Simons bosonic particle-vortex duality
• Bosonization duality in 2+1 dimensions and critical current correlation functions in Chern-Simons $U(1)\times U(1)$ Abelian Higgs model
• Functional bosonization of a Dirac field in 2+1 dimensions, in the presence of a boundary
• Superselection Rules, Bosonization Duality in 1+1 Dimensions and Momentum-Space Entanglement