Symmetry Fractionalization in Three-Dimensional ${\mathbb{Z}}_2$ Topological Order and Fermionic Symmetry-Protected Phases

Abstract

In two-dimensional topological phases, quasiparticle excitations can carry fractional symmetry quantum numbers. We generalize this notion of symmetry fractionalization to three-dimensional topological phases, in particular to loop excitations, and propose a partial classification for symmetry-enriched ${\mathbb{Z}}_2$ toric code phase. We apply the results to the classification of fermionic symmetry-protected topological phases in three dimensions.

11 pages

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• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• Symmetry fractionalization and anomaly detection in three-dimensional topological phases
• Three-dimensional anomalous twisted gauge theories with global symmetry: Implications for quantum spin liquids
• Fractionalizing Global Symmetry on Looplike Topological Excitations
• Generalized symmetry enriched criticality in (3+1)d