PIRSA:17080004 Conference Quantum Foundations Quantum Information

DOI10.48660/17080004

Conference/School: Hopf Algebras in Kitaev's Quantum Double Models: Mathematical Connections from Gauge Theory to Topological Quantum Computing and Categorical Quantum Mechanics

Dittrich, B. (2017). From 3D TQFTs to 4D models with defects. Perimeter Institute. https://pirsa.org/17080004

Dittrich, Bianca. From 3D TQFTs to 4D models with defects. Perimeter Institute, Aug. 04, 2017, https://pirsa.org/17080004 

@misc{ pirsa_PIRSA:17080004,
  doi = {10.48660/17080004},
  url = {https://pirsa.org/17080004},
  author = {Dittrich, Bianca},
  keywords = {Quantum Foundations, Quantum Information},
  language = {en},
  title = {From 3D TQFTs to 4D models with defects},
  publisher = {Perimeter Institute},
  year = {2017},
  month = {aug},
  note = {PIRSA:17080004 see, \url{https://pirsa.org}}
}

Abstract

I will explain a general strategy to lift (2+1)D topological phases, in particular string nets, to (3+1)D models with line defects. This allows a systematic construction of (3+1)D topological theories with defects, including an improved version of the Walker-Wang Model. It has also an interesting application to quantum gravity as it leads to quantum geometry realizations for which all geometric operators have discrete and bounded spectra. I will furthermore comment on some interesting (self-) duality relations that emerge in these constructions.

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