First Principle Construction of Holographic Duals

          @misc{ pirsa_11100095,
            doi = {10.48660/11100095},
            url = {https://pirsa.org/11100095},
            author = {Lee, Sung-Sik},
            keywords = {},
            language = {en},
            title = {First Principle Construction of Holographic Duals },
            publisher = {Perimeter Institute},
            year = {2011},
            month = {oct},
            note = {PIRSA:11100095 see, \url{https://pirsa.org}}
          }
          

Abstract

Topological Quantum field theories(TQFTs) are a special class of QFTs. Their actions do not depend on the metric of the background space-time manifold. Thus, it is very natural to define TQFTs on an arbitrary triangulation of the space-time manifold and they are independent on the triangulation. More importantly, TQFTs defined on triangulations are always a finite theory associated with a well defined cut-off. A well known example is the Turaev-Viro states sum invariants. Essentially, the Turaev-Viro constructions are (local) tensor network representations of a special class of 1+2D TQFTs. In this talk, I will show a new class of TQFTs that can be derived based on the (local) tensor network representations in arbitrary dimensions. They can be regarded as the discrete analogy of topological Berry phase terms of (discrete) non-linear sigma models. The edge theory of such a new class of TQFTs can be regarded as the discrete analogy of WZW terms. This new class of TQFTs naturally classify (bosonic) symmetry protected topological orders in arbitrary dimensions. Finally, I will also discuss new classes of fermionic TQFTs based on the Grassmann tensor network representations and possible new route towards Quantum Gravity(QG).