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