We consider conformal blocks of two heavy operators and an arbitrary
number of light operators in a 2d 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.
