Bosonization in 2+1 dimensions via Chern-Simons bosonic particle-vortex duality

Abstract

Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we consider a duality between lattice fermions and bosons in (2+1) spacetime dimensions, relating free massive Dirac fermions to Abelian Chern-Simons Higgs (ACSH) bosons. To establish the duality we represent the exact partition function of the lattice fermions in terms of the writhe of fermionic worldlines. On the bosonic side the partition function is expressed in the writhe of the vortex loops of the particle-vortex dual of the ACSH Lagrangian. In the continuum and scaling limit we show these to be identical. This result can be understood from the closed fermionic worldlines being direct mappings of the ACSH vortex loops, with the writhe keeping track of particle statistics.

arXiv comment13 pages, 4 figures; v2 matches published version

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Cited by in corpus (4)

• Deconfined criticality and bosonization duality in easy-plane Chern-Simons two-dimensional antiferromagnets
• Bosonization duality in 2+1 dimensions and critical current correlation functions in Chern-Simons $U(1)\times U(1)$ Abelian Higgs model
• Critical Behavior and Duality in Dimensionally Reduced Planar Chern-Simons Superconductors
• Superselection Rules, Bosonization Duality in 1+1 Dimensions and Momentum-Space Entanglement