Towards a realistic holographic tensor network: From p-adic CFT to (minimal) CFT2

          @misc{ pirsa_PIRSA:20110026,
            doi = {10.48660/20110026},
            url = {https://pirsa.org/20110026},
            author = {Hung, Ling-Yan},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Towards a realistic holographic tensor network: From p-adic CFT to (minimal) CFT2},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {nov},
            note = {PIRSA:20110026 see, \url{https://pirsa.org}}
          }
          

Abstract

The success of the Ryu-Takayanagi formula suggests a profound connection between the AdS/CFT correspondence and tensor networks. There are since many works on constructing examples, although it is very difficult to make them explicit and quantitative. We will discuss some new progress in the toy example of p-adic CFT where its tensor network dual was previously constructed explicitly [ arXiv:1703.05445 , arXiv:1812.06059, arXiv:1902.01411], and how some analogue of Einstein equation on the graph emerges as we consider RG flow of these CFTs. These progresses inspire us to find a way to construct explicit holographic tensor networks of more realistic CFTs based on their connection with topological models with one higher dimension, at least in CFT2. We will present some preliminary results and works in progress.