Higher Categorical Tools for Quantum Phases of Matter

Bosonization and anomalies of 3d fermionic topological orders

Mar 22, 2024, 10:45 a.m.

1h

PI/4-405 - Bob Room (Perimeter Institute for Theoretical Physics)

Speaker

Arun Debray (Purdue University)

Description

There are two notions of a symmetry of a group G on a 3d topological order (TO): an "algebraic" symmetry, where G acts by automorphisms on the tensor category defining the (TO), and a "field-theoretic" symmetry, where the TFT corresponding to the TO is extended to manifolds with a principal G-bundle. The "field-theoretic" notion is stronger than the "algebraic" one, and the obstruction is sometimes referred to as the anomaly of the TO. The goal of this talk is to discuss a project joint with Weicheng Ye and Matthew Yu on computing these anomalies for fermionic TOs/spin TFTs: we develop a general framework employing Gaiotto-Kapustin's bosonic shadow construction. I will discuss both the mathematical conjectures our framework rests on as well as its use in
examples. The Smith long exact sequence appears in our computations.

External references

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