Holographic Calculation for Large Interval Rényi Entropy at High Temperature

Abstract

In this paper, we study the holographic Rényi entropy of a large interval on a circle at high temperature for the two-dimensional conformal field theory (CFT) dual to pure AdS${}_3$ gravity. In the field theory, the Rényi entropy is encoded in the CFT partition function on $n$-sheeted torus connected with each other by a large branch cut. As proposed by Chen and Wu [Large interval limit of Rényi entropy at high temperature, arXiv:1412.0763], the effective way to read the entropy in the large interval limit is to insert a complete set of state bases of the twist sector at the branch cut. Then the calculation transforms into an expansion of four-point functions in the twist sector with respect to $e^{-\frac{2\pi TR}{n}}$. By using the operator product expansion of the twist operators at the branch points, we read the first few terms of the Rényi entropy, including the leading and next-to-leading contributions in the large central charge limit. Moreover, we show that the leading contribution is actually captured by the twist vacuum module. In this case by the Ward identity the four-point functions can be derived from the correlation function of four twist operators, which is related to double interval entanglement entropy. Holographically, we apply the recipe in [T. Faulkner, The entanglement Rényi entropies of disjoint intervals in AdS/CFT, arXiv:1303.7221] and [T. Barrella et al., Holographic entanglement beyond classical gravity, J. High Energy Phys. 09 (2013) 109] to compute the classical Rényi entropy and its one-loop quantum correction, after imposing a new set of monodromy conditions. The holographic classical result matches exactly with the leading contribution in the field theory up to $e^{-4\pi TR}$ and $l^6$, while the holographical one-loop contribution is in exact agreement with next-to-leading results in field theory up to $e^{-\frac{6\pi TR}{n}}$ and $l^4$ as well.

minor corrections, match with the published version

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• Holographic Rényi Entropy of Single Interval on Torus: with W symmetry
• Large Interval Limit of Rényi Entropy At High Temperature
• Entanglement entropy after selective measurements in quantum chains
• Distinguishing Black Hole Microstates using Holevo Information
• One loop partition function in AdS_3/CFT_2
• Rényi Mutual Information in Holographic Warped CFTs
• Higher spin entanglement entropy at finite temperature with chemical potential
• Monodromy methods for torus conformal blocks and entanglement entropy at large central charge
• Holographic Rényi entropy for two-dimensional N=(1,1) superconformal field theory
• Corrections to holographic entanglement plateau
• Holographic Rényi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory
• Subsystem entropy in 2d CFT and KdV ETH
• Rényi entropy at large energy density in 2D CFT
• 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
• Holographic Mutual Information of Two Disjoint Spheres
• Monstrous entanglement