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.

5 pages, typo corrected

References in corpus (4)

• "Deconfined" quantum critical points
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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