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

In this paper, we use the replica approach to study the Renyi entropy S-L 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 Renyi entropy S-R 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 S-L = S-R 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.