On short interval expansion of Rényi entropy

Abstract

Rényi entanglement entropy provides a new window to study the AdS/CFT correspondence. In this paper we consider the short interval expansion of Rényi entanglement entropy in two-dimensional conformal field theory. This amounts to do the operator product expansion of the twist operators. We focus on the vacuum Verma module and consider the quasiprimary operators constructed from the stress tensors. After obtaining the expansion coefficients of the twist operators to level 6 in vacuum Verma module, we compute the leading contributions to the Rényi entropy, to order 6 in the short interval expansion. In the case of one short interval on cylinder, we reproduce the first several leading contributions to the Rényi entropy. In the case of two short disjoint intervals with a small cross ratio $x$, we obtain not only the classical and 1-loop quantum contributions to the Rényi entropy to order $x^6$, both of which are in perfect match with the ones found in gravity, but also the leading $1/c$ contributions, which corresponds to 2-loop corrections in the bulk.

V1, 23 pages, 5 figures; V2, published version, typos corrected, references added

References in corpus (12)

• Towards a derivation of holographic entanglement entropy
• Generalized gravitational entropy
• Quantum corrections to holographic entanglement entropy
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Entanglement Entropy at Large Central Charge
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• Holographic entanglement beyond classical gravity
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• Distributional Geometry of Squashed Cones
• On generalized gravitational entropy, squashed cones and holography
• Entanglement entropy in higher derivative holography
• Note on generalized gravitational entropy in Lovelock gravity

Cited by in corpus (78)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• The Gravity Dual of Renyi Entropy
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Entanglement negativity after a global quantum quench
• Black Hole Collapse in the 1/c Expansion
• BCFT entanglement entropy at large central charge and the black hole interior
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Mutual information after a local quench in conformal field theory
• Entanglement Entropy in $T\overline{T}$-Deformed CFT
• Holographic entanglement entropy and gravitational anomalies
• Conformal Blocks and Negativity at Large Central Charge
• Holographic Rényi entropy for CFT with $W$ symmetry
• Quantum Corrections to Holographic Mutual Information
• Comments on Renyi entropy in AdS${}_3$/CFT${}_2$
• Towards entanglement negativity of two disjoint intervals for a one dimensional free fermion
• Single Interval Rényi Entropy At Low Temperature
• Renyi entropies of free bosons on the torus and holography
• On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles
• Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks
• Subsystem Trace Distance in Quantum Field Theory
• Universality of Quantum Information in Chaotic CFTs
• Partial transpose of two disjoint blocks in XY spin chains
• Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
• Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
• Probing beyond ETH at large $c$
• Bulk entanglement entropy in perturbative excited states
• Holographic partition functions and phases for higher genus Riemann surfaces
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Thermality and excited state Rényi entropy in two-dimensional CFT
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Short interval expansion of Rényi entropy on torus
• Holographic Calculation for Large Interval Rényi Entropy at High Temperature
• On the next-to-leading holographic entanglement entropy in $Ad{S}_3/CF{T}_2$
• Holographic Rényi entropy in AdS${}_3$/LCFT${}_2$ correspondence
• Rényi and Tsallis entropies: three analytic examples
• Rényi and Tsallis entropies of the Aharonov-Bohm ring in uniform magnetic fields
• On one-loop entanglement entropy of two short intervals from OPE of twist operators
• Higher Spin Entanglement Entropy
• Holographic Rényi Entropy of Single Interval on Torus: with W symmetry
• Note on ETH of descendant states in 2D CFT
• Large Interval Limit of Rényi Entropy At High Temperature
• Reflected Entropy in AdS${}_3$/WCFT
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
• An Alternative Method for Extracting the von Neumann Entropy from Renyi Entropies
• Entanglement entropy after selective measurements in quantum chains
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states
• Distinguishing Black Hole Microstates using Holevo Information
• One loop partition function in AdS_3/CFT_2
• Mutual information superadditivity and unitarity bounds
• Rényi Mutual Information in Holographic Warped CFTs
• Entanglement spectrum of geometric states
• On the Mutual Information in Conformal Field Theory
• Rényi Mutual Information for Free Scalar in Even Dimensions
• Higher spin entanglement entropy at finite temperature with chemical potential
• Double-Trace Deformations and Entanglement Entropy in AdS
• Rényi entanglement entropies for the compactified massless boson with open boundary conditions
• Holographic Rényi entropy for two-dimensional N=(1,1) superconformal field theory
• Corrections to holographic entanglement plateau
• Non-geometric States in a Holographic Conformal Field Theory
• Universality in the tripartite information after global quenches: (generalised) quantum XY models
• Relation between time- and spacelike entanglement entropy
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Sum rule for the pseudo-Rényi entropy
• Subsystem entropy in 2d CFT and KdV ETH
• Holographic Rényi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory
• Rényi entropy at large energy density in 2D CFT
• Negative R$\acute{\text{e}}$nyi entropy and Brane intersection
• Rényi Entropy for a $2d$ CFT with a gauge field: $\widehat{\mathrm{SU}}(\mathbf{N}{)}_1$ WZW theory on a branched torus
• Note on Bulk Reconstruction in AdS${}_3$/WCFT${}_2$
• Rényi entropies of the massless Dirac field on the torus
• Rényi Entropy for the $\sun1$ WZW model on the torus
• Holographic Mutual Information of Two Disjoint Spheres
• Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT
• Perturbative distinguishability of black hole microstates from AdS/CFT correspondence
• $2$-Rényi CCNR Negativity of Compact Boson for multiple disjoint intervals
• Subsystem fidelity in two-dimensional conformal field theories
• Note on Mutual Information between Two Intervals of Extremal BTZ