Thermal corrections to Rényi entropies for conformal field theories

We compute thermal corrections to Rényi entropies of d dimensional conformal field theories on spheres. Consider the n th Rényi entropy for a cap of opening angle 2 θ on S d −1 . From a Boltzmann sum decomposition and the operator-state correspondence, the leading correction is related to a certain two-point correlation function of the operator (not equal to the identity) with smallest scaling dimension. More specifically, via a conformal map, the correction can be expressed in terms of the two-point function on a certain conical space with opening angle 2 πn . In the case of free conformal field theories, this two-point function can be computed explicitly using the method of images. We perform the computation for the conformally coupled scalar. From the n → 1 limit of our results, we extract the leading thermal correction to the entanglement entropy, reproducing results of arXiv:1407.1358