Gravitational dual of the Rényi twist displacement operator

Abstract

We give a recipe for computing correlation functions of the displacement operator localized on a spherical or planar higher dimensional twist defect using AdS/CFT. Such twist operators are typically used to construct the $n$'th Renyi entropies of spatial entanglement in CFTs and are holographically dual to black holes with hyperbolic horizons. The displacement operator then tells us how the Renyi entropies change under small shape deformations of the entangling surface. We explicitly construct the bulk to boundary propagator for the displacement operator insertion as a linearized metric fluctuation of the hyperbolic black hole and use this to extract the coefficient of the displacement operator two point function $C_D$ in any dimension. The $n\to 1$ limit of the twist displacement operator gives the same bulk response as the insertion of a null energy operator in vacuum, which is consistent with recent results on the shape dependence of entanglement entropy and modular energy.

6 pages plus appendices, 2 figures

References in corpus (11)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Towards a derivation of holographic entanglement entropy
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Universality of corner entanglement in conformal field theories
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Wilson loop correlators at strong coupling: from matrices to bubbling geometries
• Universality in the geometric dependence of Renyi entropy
• Renyi Entropy and Geometry
• Gravity duals of boundary cones

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• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• Monodromy Defects from Hyperbolic Space
• 6d surface defects from massive type IIA
• Exact Bremsstrahlung functions in ABJM theory
• Marginal deformations and defect anomalies
• Defect multiplets of N=1 supersymmetry in 4d
• Quantum Error Correction in SYK and Bulk Emergence