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

Higher-point conformal blocks and entanglement entropy in heavy states