Holographic Rényi Entropy of Single Interval on Torus: with W symmetry

Abstract

In this paper, we extend our study of the holographic Rényi entropy of single interval on a torus to the CFT with W symmetry. To read the possible corrections from W fields clearly, we compute the thermal correction to the Rényi entropy up to the order $e^{-8\pi /TL}$. In the field theory, this requires us to compute the contribution from all the level 4 states, from both the vacuum module and W primaries. On the gravity side, after computing the eigenvalue of single Schottky generators to the order $e^{-4\pi /TL}$, we obtain the 1-loop quantum correction to the holographic Rényi entropy. We find complete agreement between the bulk and boundary theories.

14 pages

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• One loop partition function in AdS_3/CFT_2
• Higher spin entanglement entropy at finite temperature with chemical potential
• Corrections to holographic entanglement plateau
• Holographic Rényi entropy for two-dimensional N=(1,1) superconformal field theory
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Holographic Rényi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory
• Rényi Entropy for a $2d$ CFT with a gauge field: $\widehat{\mathrm{SU}}(\mathbf{N}{)}_1$ WZW theory on a branched torus
• Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT
• Rényi Entropy for the $\sun1$ WZW model on the torus
• Monstrous entanglement