PIRSA:24030092 Conference Condensed Matter

DOI10.48660/24030092

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

Burnell, F. (2024). Models of anyons with symmetry: a bulk-boundary correspondence. Perimeter Institute. https://pirsa.org/24030092

Burnell, Fiona. Models of anyons with symmetry: a bulk-boundary correspondence. Perimeter Institute, Mar. 18, 2024, https://pirsa.org/24030092 

@misc{ pirsa_PIRSA:24030092,
  doi = {10.48660/24030092},
  url = {https://pirsa.org/24030092},
  author = {Burnell, Fiona},
  keywords = {Condensed Matter},
  language = {en},
  title = {Models of anyons with symmetry: a bulk-boundary correspondence},
  publisher = {Perimeter Institute},
  year = {2024},
  month = {mar},
  note = {PIRSA:24030092 see, \url{https://pirsa.org}}
}

Abstract

I will describe models with on-site symmetry that permutes anyons with non-trivial mutual statistics, and show that the action of this symmetry on the boundary can effectively be that of a non-invertible symmetry such as Kramers-Wannier duality. I will sketch some implications of this for anomalies in non-invertible symmetries. Finally, I will introduce a construction (based on idempotent completion) that allows us to realize all possible anyon permuting symmetries of a given topological order in an on-site way.

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