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

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