Thermal Corrections to R enyi Entropies for

We compute thermal corrections to R enyi entropies of d dimensional conformal eld theories on spheres. Consider the nth R enyi entropy for a cap of opening angle 2 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 specically, via a conformal map, the correction can be expressed in terms of the two-point function on a certain conical space with opening angle 2n . In the case of free conformal eld 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.