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arXiv · 1411.6505

Thermal Corrections to Renyi Entropies for Conformal Field Theories

Christopher P. Herzog·Jun Nian
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Abstract

We compute thermal corrections to R\'enyi entropies of $d$ dimensional conformal field theories on spheres. Consider the $n$th R\'enyi 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.

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Christopher P. Herzog, Jun Nian. 2014-11-24. Thermal Corrections to Renyi Entropies for Conformal Field Theories. https://doi.org/10.1007/jhep06(2015)009

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