Topological Insulators Avoid the Parity Anomaly

Abstract

The surface of a 3+1d topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2+1d system, this surface theory would necessarily explicitly break parity and time-reversal when coupled to a fluctuating gauge field. Here we explain why such a state can exist on the boundary of a 3+1d system without breaking these symmetries, even if the number of boundary components is odd. This is accomplished from two complementary perspectives: topological quantization conditions and regularization. We first discuss the conditions under which (continuous) large gauge transformations may exist when the theory lives on a boundary of a higher-dimensional spacetime. Next, we show how the higher-dimensional bulk theory is essential in providing a parity-invariant regularization of the theory living on the lower-dimensional boundary or defect.

46 pages, 1 figure, harvmac

References in corpus (6)

• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Comments on Chern-Simons Contact Terms in Three Dimensions
• Fractional topological insulators in three dimensions

Cited by in corpus (40)

• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Is the Composite Fermion a Dirac Particle?
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Bosonization and Mirror Symmetry
• Large dynamical axion field in topological antiferromagnetic insulator Mn${}_2$Bi${}_2$Te${}_5$
• Mirror symmetry and the half-filled Landau level
• Half-Quantized Hall Effect and Power Law Decay of Edge Current Distribution
• Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface
• Gravitational parity anomaly with and without boundaries
• Survival of the quantum anomalous Hall effect in orbital magnetic fields as a consequence of the parity anomaly
• The quest for Casimir repulsion between Chern-Simons surfaces
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Duality and Universal Transport in a Mixed-Dimension Electrodynamics
• Anisotropic topological magnetoelectric effect in axion insulators
• Quantum Field Theory Anomalies in Condensed Matter Physics
• Parity anomaly in four dimensions
• Superconformal Models for Graphene and Boundary Central Charges
• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Functional Approach to Electrodynamics of Media
• Perfect Metal Phases of One-Dimensional and Anisotropic Higher-Dimensional Systems
• Quantum Dirac fermions in half space and their interaction with electromagnetic field
• Fate of Quantum Anomalous Hall Effect in the Presence of External Magnetic Fields and Particle-Hole Asymmetry
• A note on the parity anomaly from the Hamiltonian point of view
• Time-reversal-symmetric topological magnetoelectric effect in three-dimensional topological insulators
• Three-dimensional Topological Insulators and Bosonization
• Dirac fermion duality and the parity anomaly
• Fractional Fermion Number and Hall Conductivity of Domain Walls
• Topological Magnetoelectric Effect: Nonlinear Time-Reversal-Symmetric Response, Witten Effect, and Half-Integer Quantum Hall Effect
• Spectral asymmetry induces a re-entrant quantum Hall effect in a topological insulator
• Dynamical magnetoelectric coupling in axion insulator thin films
• Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect
• Capacitive scheme to detect the topological magnetoelectric effect
• Thermoelectric properties and Wiedemann-Franz like relations in mixed-dimensional QEDs from particle-vortex dualities
• On the Electromagnetic Response of Topological Superconductors
• Anti-commutative dynamical magneto-electric response in certain solid state materials
• Absence of Parity Anomaly in Massive Dirac Fermions on a Lattice
• Dual QED3 at "NF = 1/2" is an interacting CFT in the infrared
• Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases
• Parity Anomaly of Lattice Maxwell Fermions in Two Spatial Dimensions