Thermal Corrections to Renyi Entropies for Conformal Field Theories

Abstract

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 $2\theta$ 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 $2\pi n$. 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 $n\to 1$ limit of our results, we extract the leading thermal correction to the entanglement entropy, reproducing results of arXiv:1407.1358.

18 pages, 5 figures; v2 reference added

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• Renormalized Entanglement Entropy on Cylinder
• Thermal Corrections to Rényi Entropy in BMS Field Theory
• Thermal Corrections to Rényi entropies for Free Fermions
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Exact Multi-Instanton Solutions to Selfdual Yang-Mills Equation on Curved Spaces