  We study the R\'enyi entropies of N disjoint intervals in the conformal field
theories given by the free compactified boson and the Ising model. They are
computed as the 2N point function of twist fields, by employing the partition
function of the model on a particular class of Riemann surfaces. The results
are written in terms of Riemann theta functions. The prediction for the free
boson in the decompactification regime is checked against exact results for the
harmonic chain. For the Ising model, matrix product states computations agree
with the conformal field theory result once the finite size corrections have
been taken into account.
