Parity anomaly cancellation in a three-dimensional QED with single massless Dirac fermion

Abstract

We study a three-dimensional non-compact QED with a single two-component massless fermion and two infinitely massive regulator fermions of half the charge using lattice overlap formalism. The parity anomaly is expected to cancel exactly between the massless and regulator fermions in the continuum, but this cancellation is inexact on lattice akin to lattice chiral gauge theories. We show non-perturbatively that parity-breaking terms vanish in the continuum limit at any finite volume. We present numerical evidences that the resulting parity-invariant theory spontaneously breaks parity in the infinite volume limit.

V2: matches the version to be published in PRL

References in corpus (2)

• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
• Phase of the fermion determinant in QED_3 using a gauge invariant lattice regularization

Cited by in corpus (11)

• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor
• Pseudo Quantum Electrodynamics and Chern-Simons theory Coupled to Two-dimensional Electrons
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Antiparticles as particles: QED${}_{2+1}$ and composite Fermions at $\nu =\frac{1}{2}$
• Non-cancellation of the parity anomaly in the strong-field regime of QED${}_{2+1}$
• The relevance of the three dimensional Thirring coupling at finite temperature and density
• Random matrix approach to three-dimensional QCD with a Chern-Simons term
• Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions
• Topological gauge actions on the lattice as Overlap fermion determinants