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Thermal Corrections to Renyi Entropies for Conformal Field Theories · Around

2014

Thermal Corrections to Renyi Entropies for Conformal Field Theories

Herzog, Christopher P., Nian, Jun

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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 $2\pi n$.

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