Würzburg Seminar on Quantum Field Theory and Gravity

I will describe how topological orders in d+1 dimensions can be used to construct RG operators that preserve certain topological symmetries for QFT in d dimensions. By constructing the eigenstates of these RG operators, we recover analytic holographic tensor networks that reproduce the continuous CFT exactly. The reason why it works follows from the factorisation properties of CFT. We show that in the case of Liouville theory, the resultant TQFT in the bulk can be thought of as a Turaev-Viro formulation of the Teichumuller TQFT.