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

Chinese University of Hong Kong

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 If time permits, I will also discuss some unpublished results on irrational CFT and even complex CFT. Our results open a new door towards understanding CFT in higher dimensions.