Holographic calculations of Rényi entropy

We extend the approach of [12] to a new calculation of the Rényi entropy of a general CFT in d dimensions with a spherical entangling surface, in terms of certain thermal partition functions. We apply this approach to calculate the Rényi entropy in various holographic models. Our results indicate that in general, the Rényi entropy will be a complicated nonlinear function of the central charges and other parameters which characterize the CFT. We also exhibit the relation between this new thermal calculation and a conventional calculation of the Rényi entropy where a twist operator is inserted on the spherical entangling surface. The latter insight also allows us to calculate the scaling dimension of the twist operators in the holographic models.