  We extend the approach of Casini, Huerta and Myers to a new calculation of
the Renyi 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 Renyi entropy in various holographic models. Our
results indicate that in general, the Renyi 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 Renyi 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.
