Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d

Abstract

We study gapped systems with anomalous time-reversal symmetry and global gravitational anomaly in three and four spacetime dimensions. These systems describe topological order on the boundary of bosonic Symmetry Protected Topological (SPT) Phases. Our description of these phases is via the recent cobordism proposal for their classification. In particular, the behavior of these systems is determined by the geometry of Stiefel-Whitney classes. We discuss electric and magnetic operators defined by these classes, and new types of Wilson lines and surfaces that sit on their boundary. The lines describe fermionic particles, while the surfaces describe a sort of fermionic string. We show that QED with a fermionic monopole exhibits the 4d global gravitational anomaly and has a fermionic $\pi$-flux.

17 pages, 7 figures, comments encouraged; significantly reworked version, designed to reach a wider audience and with new sections on fermionic monopoles in 4d and Stiefel-Whitney operators

References in corpus (4)

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Boson topological insulators: A window into highly entangled quantum phases
• Classification of interacting electronic topological insulators in three dimensions
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order

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• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
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• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
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• Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions
• Anomaly of the Electromagnetic Duality of Maxwell Theory
• Minimal nondegenerate extensions
• All-fermion electrodynamics and fermion number anomaly inflow
• Lorentz Symmetry Fractionalization and Dualities in (2+1)d
• Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
• Symmetry enriched U(1) quantum spin liquids
• On gapped boundaries for SPT phases beyond group cohomology
• Line Operators of Gauge Theories on Non-Spin Manifolds
• TQFT, Symmetry Breaking, and Finite Gauge Theory in 3+1D
• Gravitational anomaly of 3+1 dimensional Z_2 toric code with fermionic charges and fermionic loop self-statistics
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Higher Berry Phase of Fermions and Index Theorem
• Toric 2-group anomalies via cobordism
• Symmetry-preserving boundary of (2+1)D fractional quantum Hall states
• 3+1d Boundaries with Gravitational Anomaly of 4+1d Invertible Topological Order for Branch-Independent Bosonic Systems
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• Matching higher symmetries across Intriligator-Seiberg duality
• Anomalies and symmetry fractionalization in reflection-symmetric topological order
• Anomaly constraint on chiral central charge of (2+1)d topological order
• A QCA for every SPT
• Generalized Statistics on Lattices
• 2-Drinfel'd double symmetry of the 4d Kitaev model
• Anomalies of global symmetries on the lattice
• Generalized symmetry enriched criticality in (3+1)d
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• Loops in 4+1d Topological Phases