PIRSA:24030079 Conference Condensed Matter

DOI10.48660/24030079

Conference/School: Higher Categorical Tools for Quantum Phases of Matter

Debray, A. (2024). Bosonization and anomalies of 3d fermionic topological orders. Perimeter Institute. https://pirsa.org/24030079

Debray, Arun. Bosonization and anomalies of 3d fermionic topological orders. Perimeter Institute, Mar. 22, 2024, https://pirsa.org/24030079 

@misc{ pirsa_PIRSA:24030079,
  doi = {10.48660/24030079},
  url = {https://pirsa.org/24030079},
  author = {Debray, Arun},
  keywords = {Condensed Matter},
  language = {en},
  title = {Bosonization and anomalies of 3d fermionic topological orders},
  publisher = {Perimeter Institute},
  year = {2024},
  month = {mar},
  note = {PIRSA:24030079 see, \url{https://pirsa.org}}
}

Abstract

here 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.

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