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

Authors :
Flavio S. Nogueira
Jeroen van den Brink
Oguz Turker
Tobias Meng
Source :
Physical Review
Publication Year :
2020
Publisher :
American Physical Society (APS), 2020.

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.<br />Comment: 13 pages, 4 figures; v2 matches published version

Details

ISSN :
24700029 and 24700010
Volume :
102
Database :
OpenAIRE
Journal :
Physical Review D
Accession number :
edsair.doi.dedup.....0f195d0d56d3e1d8d5af1278935b3206
Full Text :
https://doi.org/10.1103/physrevd.102.034506