A gauge theory generalization of the fermion-doubling theorem

Abstract

It is possible to characterize certain states of matter by properties of their edge states. This implies a notion of `surface-only models': models which can only be regularized at the edge of a higher-dimensional system. After incorporating the fermion-doubling results of Nielsen and Ninomiya into this framework, we employ this idea to identify new obstructions to symmetry-preserving regulators of quantum field theory. We focus on an example which forbids regulated models of Maxwell theory with manifest electromagnetic duality symmetry.

10 pages

References in corpus (13)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Boson topological insulators: A window into highly entangled quantum phases
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Heisenberg Groups and Noncommutative Fluxes
• Holographic Action for the Self-Dual Field
• Wave Functions of Bosonic Symmetry Protected Topological Phases
• Classification of abelian spin Chern-Simons theories
• Conformal blocks for AdS5 singletons
• Local electromagnetic duality and gauge invariance
• Anyonic strings and membranes in AdS space and dual Aharonov-Bohm effects
• No local Maxwell duality invariance

Cited by in corpus (25)

• Generalized Global Symmetries
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Generalized global symmetries and holography
• Revealing tensor monopoles through quantum-metric measurements
• Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States
• Universal Features of Higher-Form Symmetries at Phase Transitions
• 6D Fractional Quantum Hall Effect
• Anomaly of the Electromagnetic Duality of Maxwell Theory
• All-fermion electrodynamics and fermion number anomaly inflow
• Symmetry enriched U(1) quantum spin liquids
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Holography in flat spacetime: 4D theories and electromagnetic duality on the border
• On the introduction of a boundary in topological field theories
• Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications
• Theory of oblique topological insulators
• Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases
• Bosonic Short Range Entangled states Beyond Group Cohomology classification
• Phase structure of self-dual lattice gauge theories in 4d
• Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
• Quantum Information Theory of the Gravitational Anomaly
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models
• Model of Fractionalization of Faraday Lines in Compact Electrodynamics
• Loops in 4+1d Topological Phases