Higher-point conformal blocks and entanglement entropy in heavy states

We consider conformal blocks of two heavy operators and an arbitrary number of light operators in a (1+1)-d CFT with large central charge. Using the monodromy method, these higher-point conformal blocks are shown to factorize into products of 4 point conformal blocks in the heavy-light limit for a class of OPE channels. This result is reproduced by considering suitable worldline configurations in the bulk conical defect geometry. We apply the CFT results to calculate the entanglement entropy of an arbitrary number of disjoint intervals for heavy states. The corresponding holographic entanglement entropy calculated via the minimal area prescription precisely matches these results from CFT. Along the way, we briefly illustrate the relation of these conformal blocks to Riemann surfaces and their associated moduli space.