Dirac fermion duality and the parity anomaly

Abstract

We present a derivation of the recently discovered duality between the free massless (2+1)-dimensional Dirac fermion and QED${}_3$. Our derivation is based on a regularized lattice model of the Dirac fermion and is similar to the more familiar derivation of the boson-vortex duality. It also highlights the important role played by the parity anomaly, which is somewhat less obvious in other discussions of this duality in the literature.

arXiv comment5 pages, typo corrected

References in corpus (19)

• "Deconfined" quantum critical points
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• Is the Composite Fermion a Dirac Particle?
• Deconfined quantum critical points: symmetries and dualities
• Slave-rotor mean field theories of strongly correlated systems and the Mott transition in finite dimensions
• Particle-Vortex Duality from 3d Bosonization
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Dual Dirac liquid on the surface of the electron topological insulator
• Putting competing orders in their place near the Mott transition
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• The half-filled Landau level: the case for Dirac composite fermions
• Mott transition between a spin-liquid insulator and a metal in three dimensions
• Vortices and quasiparticles near the "superconductor-insulator" transition in thin films
• Exact Boson-Fermion Duality on a 3D Euclidean Lattice
• Topological Insulators Avoid the Parity Anomaly
• Superfluid-Insulator Transitions on the Triangular Lattice
• Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
• Lattice model for the surface states of a topological insulator with applications to magnetic and exciton instabilities

Cited by in corpus (9)

• Half-Quantized Hall Effect and Power Law Decay of Edge Current Distribution
• Charge density waves in Weyl semimetals
• Altermagnetism-Induced Parity Anomaly in Weak Topological Insulators
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Quarter-quantized thermal Hall effect with parity anomaly
• Signature of parity anomaly in the measurement of optical Hall conductivity in quantum anomalous Hall systems
• Fermion-fermion duality in 3+1 dimensions
• Antiparticles as particles: QED${}_{2+1}$ and composite Fermions at $\nu =\frac{1}{2}$
• Fermionic dualities with axial gauge fields