1. Bosonization in 2+1 dimensions via Chern-Simons bosonic particle-vortex duality
- Author
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Flavio S. Nogueira, Jeroen van den Brink, Oguz Turker, and Tobias Meng
- Subjects
High Energy Physics - Theory ,Condensed Matter::Quantum Gases ,Bosonization ,Physics ,Particle statistics ,Statistical Mechanics (cond-mat.stat-mech) ,010308 nuclear & particles physics ,High Energy Physics::Lattice ,Chern–Simons theory ,FOS: Physical sciences ,Fermion ,01 natural sciences ,Scaling limit ,High Energy Physics - Theory (hep-th) ,0103 physical sciences ,Higgs boson ,010306 general physics ,Condensed Matter - Statistical Mechanics ,Mathematical physics ,Writhe ,Boson - 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., Comment: 13 pages, 4 figures; v2 matches published version
- Published
- 2020
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