PIRSA:14040099

Grassmann tensor network renormalization and fermionic topological quantum field theory: a new route towards quantum gravity

Gu, Z. (2014). Grassmann tensor network renormalization and fermionic topological quantum field theory: a new route towards quantum gravity. Perimeter Institute. https://pirsa.org/14040099

Gu, Zheng-Cheng. Grassmann tensor network renormalization and fermionic topological quantum field theory: a new route towards quantum gravity. Perimeter Institute, Apr. 24, 2014, https://pirsa.org/14040099 

          @misc{ pirsa_PIRSA:14040099,
            doi = {10.48660/14040099},
            url = {https://pirsa.org/14040099},
            author = {Gu, Zheng-Cheng},
            keywords = {},
            language = {en},
            title = {Grassmann tensor network renormalization and fermionic topological quantum field theory: a new route towards quantum gravity},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {apr},
            note = {PIRSA:14040099 see, \url{https://pirsa.org}}
          }

Zheng-Cheng Gu Chinese University of Hong Kong

DOI 10.48660/14040099
Collection
Talk Type Conference

Abstract

Recently, the development of tensor network renormalization approach has provided us a powerful tool to construct new classes of topological quantum field theories(TQFTs) in discrete space-time. For example, the Turaev Viro’s states sum constructions are fixed point tensor networks representing a special class of 2+1D TQFTs. Interestingly, the Grassmann variable generalization of tensor network renormalization approach leads to new classes of TQFTs for interacting fermion systems, namely, the fermionic TQFTs. In this talk, I will start with a fermionic topological nonlinear sigma model and discuss its corresponding new mathematics - group super-cohomology theory. Then I will explain the fermionic generalization of Dijkgraaf -Witten gauge theory by using group supercohomology theory. Finally I will show examples beyond fermionic Dijkgraaf -Witten gauge theory and discuss possible new routes towards quantum gravity.