Towards the generalized gravitational entropy for spacetimes with non-Lorentz invariant duals

Abstract

Based on the Lewkowycz-Maldacena prescription and the fine structure analysis of holographic entanglement proposed in arXiv:1803.05552, we explicitly calculate the holographic entanglement entropy for warped CFT that duals to AdS${}_3$ with a Dirichlet-Neumann type of boundary conditions. We find that certain type of null geodesics emanating from the entangling surface $\partial \mathcal{A}$ relate the field theory UV cutoff and the gravity IR cutoff. Inspired by the construction, we furthermore propose an intrinsic prescription to calculate the generalized gravitational entropy for general spacetimes with non-Lorentz invariant duals. Compared with the RT formula, there are two main differences. Firstly, instead of requiring that the bulk extremal surface $\mathcal{E}$ should be anchored on $\partial \mathcal{A}$, we require the consistency between the boundary and bulk causal structures to determine the corresponding $\mathcal{E}$. Secondly we use the null geodesics (or hypersurfaces) emanating from $\partial \mathcal{A}$ and normal to $\mathcal{E}$ to regulate $\mathcal{E}$ in the bulk. We apply this prescription to flat space in three dimensions and get the entanglement entropies straightforwardly.

arXiv comment40pages,16 figures; v2 version improved, a discussion section added, references added; v3 minor corrections, matching the published version on JHEP

References in corpus (54)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Aspects of Holographic Entanglement Entropy
• A Covariant Holographic Entanglement Entropy Proposal
• The holographic principle
• Towards a derivation of holographic entanglement entropy
• The dS/CFT Correspondence
• Generalized gravitational entropy
• Gravity duals for non-relativistic CFTs
• On BMS Invariance of Gravitational Scattering
• Aspects of the BMS/CFT correspondence
• Causality & holographic entanglement entropy
• Warped AdS_3 Black Holes
• The BMS/GCA correspondence
• Deriving covariant holographic entanglement
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Entanglement entropy in Galilean conformal field theories and flat holography
• Lifshitz holography
• On String Theory Duals of Lifshitz-like Fixed Points
• New Boundary Conditions for AdS3
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Lifshitz Gravity for Lifshitz Holography
• Entanglement Entropy in Flat Holography
• Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity
• Entropy, Extremality, Euclidean Variations, and the Equations of Motion
• Warped Conformal Field Theory as Lower Spin Gravity
• Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
• Entanglement contour
• Entanglement Entropy in Warped Conformal Field Theories
• Modifications to Holographic Entanglement Entropy in Warped CFT
• General properties of holographic entanglement entropy
• Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations
• Holographic thermalization with Lifshitz scaling and hyperscaling violation
• Holographic Entanglement and Poincare blocks in three dimensional flat space
• Schrödinger Holography with and without Hyperscaling Violation
• The nuts and bolts of the BMS Bootstrap
• Correlation Functions of Warped CFT
• Geodesic Diagrams, Gravitational Interactions & OPE Structures
• Locality and anomalies in warped conformal field theory
• Two Virasoro symmetries in stringy warped AdS${}_3$
• Chiral Liouville Gravity
• Entanglement Evolution in Lifshitz-type Scalar Theories
• Entanglement Entropy in Lifshitz Theories
• Generalized Gravitational Entropy for Warped Anti-de Sitter Space
• Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms
• Entanglement Entropy in Non-Relativistic Field Theories
• The imaginary part of the gravity action and black hole entropy
• Semi-classical BMS${}_3$ blocks and flat holography
• Topological aspects of generalized gravitational entropy
• On the reconstruction of Lifshitz spacetimes
• Lifshitz entanglement entropy from holographic cMERA
• Complex Entangling Surfaces for AdS and Lifshitz Black Holes?
• Holographic Calculation of BMSFT Mutual and 3-partite Information

Cited by in corpus (33)

• Holographic entanglement contour, bit threads, and the entanglement tsunami
• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Swing surfaces and holographic entanglement beyond AdS/CFT
• Entanglement Wedge in Flat Holography and Entanglement Negativity
• Warped Information and Entanglement Islands in AdS/WCFT
• Balanced Partial Entanglement and Mixed State Correlations
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Entanglement entropy from entanglement contour: higher dimensions
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Entanglement and chaos in warped conformal field theories
• Formulas for Partial Entanglement Entropy
• The PEE aspects of entanglement islands from bit threads
• Local measures of entanglement in black holes and CFTs
• Entanglement contour and modular flow from subset entanglement entropies
• Deriving the PEE proposal from the Locking bit thread configuration
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
• Ownerless island and partial entanglement entropy in island phases
• Gravitation in flat spacetime from entanglement
• Reflected Entropy in AdS${}_3$/WCFT
• Rényi Mutual Information in Holographic Warped CFTs
• Supersymmetric Warped Conformal Field Theory
• Geometrizing the Partial Entanglement Entropy: from PEE Threads to Bit Threads
• First Law of Entanglement Entropy in Flat-Space Holography
• Entanglement after Quantum Quenches in Lifshitz Scalar Theories
• Warped Conformal Symmetries of the Accelerating Kerr Black Hole
• Squashed Entanglement from Generalized Rindler Wedge
• Weaving the (AdS) spaces with partial entanglement entropy threads
• First Law and Quantum Correction for Holographic Entanglement Contour
• Flat-space Limit of Extremal Curves
• Entanglement Negativity in Flat Holography
• Warped CFT duals of the Plebański-Demiański family of solutions
• Gravitational radiations of Kerr black hole from warped symmetries
• Holographic Tensor Networks as Tessellations of Geometry