Fixed-point tensor network construction and generalized symmetry for conformal field theory

The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real space renormalization group (RG) scheme. In this talk, I will present an explicit analytical construction of the fixed point(FP) tensor for 2D rational CFT. We define it as a correlation function between the "boundary-changing operators" on triangles. Our construction fully captures all the real-space RG conditions. We also provide a concrete example using the several models to compute the scaling dimensions explicitly. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture and generalize symmetries naturally emerge. If time permits, I will also discuss some recent results on irrational CFT and a topological bootstrap method based on algebraic tensor network.