PIRSA:24030089 Conference Condensed Matter

DOI10.48660/24030089

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

Omori, K. (2024). Categorical Aspects of Symmetry in Fermionic Systems. Perimeter Institute. https://pirsa.org/24030089

Omori, Kantaro. Categorical Aspects of Symmetry in Fermionic Systems. Perimeter Institute, Mar. 21, 2024, https://pirsa.org/24030089 

@misc{ pirsa_PIRSA:24030089,
  doi = {10.48660/24030089},
  url = {https://pirsa.org/24030089},
  author = {Omori, Kantaro},
  keywords = {Condensed Matter},
  language = {en},
  title = {Categorical Aspects of Symmetry in Fermionic Systems},
  publisher = {Perimeter Institute},
  year = {2024},
  month = {mar},
  note = {PIRSA:24030089 see, \url{https://pirsa.org}}
}

Abstract

In this talk we explore the symmetry in 1+1d fermionic systems from a category theory perspective. We argue that It requires additional structure than a tensor category over sVect, and rather captured by a fusion category equipped with a braided central functor from a specific braided fusion category, dependent on the chiral central charge. The same data defines a 1-morphism in the 4-category of braided tensor categories, which lead us to a 4d-3d-2d picture via cobordism hypothesis. This talk is based on an ongoing work with K. Inamura.

Resources

Next talk

Related Talks