Entanglement entropy in (1+1)D CFTs with multiple local excitations

In this paper, we use the replica approach to study the Rényi entropy SL of generic locally excited states in (1+1)D CFTs, which are constructed from the insertion of multiple product of local primary operators on vacuum. Alternatively, one can calculate the Rényi entropy SR corresponding to the same states using Schmidt decomposition and operator product expansion, which reduces the multiple product of local primary operators to linear combination of operators. The equivalence SL = SR translates into an identity in terms of the F symbols and quantum dimensions for rational CFT, and the latter can be proved algebraically. This, along with a series of papers, gives a complete picture of how the quantum information quantities and the intrinsic structure of (1+1)D CFTs are consistently related.