Abstract
The key property of fermionic topological order is that fermions can be created by local operators; any action of a global symmetry group $G_f$ must respect this property. We construct an algebraic formalism for symmetry fractionalization in fermionic symmetry-enriched topological phases (FSETs). Our formalism is similar to a bosonic theory of $G_b = G_f/Z_2^F$ symmetry fractionalization, where $Z_2^F$ is the group generated by fermion parity symmetry, but with constraints that enforce the locality of the fermion. We characterize the obstructions to and classification of fermionic symmetry fractionalization. We then algebraically describe the ‘t Hooft anomaly of an FSET, that is, the obstruction to gauging $G_f$. To do so, we first gauge fermion parity, and then find a four-step sequence of obstructions to extending $G_b$ symmetry to the parity-gauged theory. We discuss an anomaly inflow argument characterizing some anomalous (2+1)D FSETs as surface theories for (3+1)D fermionic symmetry-protected topological phases.
Biography
Danny Bulmash is currently a postdoctoral researcher at University of Maryland at College Park. He got his PhD from Stanford University in 2017. He has been working on and made important contributions to various aspects of topological phases of matter including fractons, higher-rank gauge theories, and quantum anomalies.
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