  Two-dimensional conformal field theories with a large central charge and a
small number of low-dimension operators are studied using the conformal block
expansion. A universal formula is derived for the Renyi entropies of N disjoint
intervals in the ground state, valid to all orders in a series expansion. This
is possible because the full perturbative answer in this regime comes from the
exchange of the stress tensor and other descendants of the vacuum state.
Therefore, the Renyi entropy is related to the Virasoro vacuum block at large
central charge. The entanglement entropy, computed from the Renyi entropy by an
analytic continuation, decouples into a sum of single-interval entanglements.
This field theory result agrees with the Ryu-Takayanagi formula for the
holographic entanglement entropy of a 2d CFT, applied to any number of
intervals, and thus can be interpreted as a microscopic calculation of the area
of minimal surfaces in 3d gravity.
