The boundary dual of the bulk symplectic form
arXiv:1806.10144 · doi:10.1016/j.physletb.2018.10.071
Abstract
In this paper, we study the overlaps of wavefunctionals prepared by turning on sources in the Euclidean path integral. For nearby states, these overlaps give rise to a Kahler structure on the space of sources, which is naturally induced by the Fubini-Study metric. The Kahler form obtained this way can also be thought of as a Berry curvature and, for holographic field theories, we show that it is identical to the gravitational symplectic form in the bulk. We discuss some possible applications of this observation, in particular a boundary prescription to calculate the variation of the volume of a maximal slice.
arXiv comment6 pages, 1 figure, v2: published version
References in corpus (16)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
- Complexity Equals Action
- On Black Hole Entropy
- On the Holographic Renormalization Group
- Relative entropy equals bulk relative entropy
- Holographic representation of local bulk operators
- Holographic Entanglement Entropy
- Real-time gauge/gravity duality: Prescription, Renormalization and Examples
- Entanglement Equilibrium and the Einstein Equation
- The Holographic Renormalization Group
- Gravity Dual of Quantum Information Metric
- From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
- On excited states in real-time AdS/CFT
- Geometric Microstates for the Three Dimensional Black Hole?
- A Note On Boundary Conditions In Euclidean Gravity
Cited by in corpus (54)
- Quantum Computation as Gravity
- Covariant phase space with boundaries
- Holographic Pseudo Entropy
- Does Complexity Equal Anything?
- Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
- Complexity and the bulk volume, a new York time story
- Holographic Complexity Equals Which Action?
- The First Law of Complexity
- Path integral optimization as circuit complexity
- Gravitational Thermodynamics of Causal Diamonds in (A)dS
- Complexity for Conformal Field Theories in General Dimensions
- Complexity Equals Anything II
- Cosmological Complexity
- Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
- Aspects of The First Law of Complexity
- Edge modes as reference frames and boundary actions from post-selection
- Complexity of Holographic Superconductors
- A Modular Sewing Kit for Entanglement Wedges
- Lorentzian threads as 'gatelines' and holographic complexity
- Gravitational path integral from the deformation
- Quantum complexity in gravity, quantum field theory, and quantum information science
- Does Boundary Distinguish Complexities?
- Time evolution of the complexity in chaotic systems: concrete examples
- Circuit complexity for generalised coherent states in thermal field dynamics
- Binding Complexity and Multiparty Entanglement
- Wheeler-DeWitt states of the AdS-Schwarzschild interior
- Complexity=Anything: Singularity Probes
- Emergent classical spacetime from microstates of an incipient black hole
- Holographic excited states in AdS Black Holes
- Modular Hamiltonian for (holographic) excited states
- Computing spacetime
- Bootstrapping Quantum Extremal Surfaces I: The Area Operator
- Circuit Complexity in Topological Quantum Field Theory
- Revisit on holographic complexity in two-dimensional gravity
- The Holographic Dual of the Entanglement Wedge Symplectic Form
- Entanglement spectrum of geometric states
- Virasoro Entanglement Berry Phases
- Unambiguous Phase Spaces for Subregions
- From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT
- The first law of differential entropy and holographic complexity
- Rényi entropies and area operator from gravity with Hayward term
- Emergent Gravity in a Holographic Universe
- Stringy Effects and the Role of the Singularity in Holographic Complexity
- Islands and Uhlmann phase: Explicit recovery of classical information from evaporating black holes
- To be unitary-invariant or not?: a simple but non-trivial proposal for the complexity between states in quantum mechanics/field theory
- Toward Krylov-based holography in double-scaled SYK
- Interior analysis, stretched technique and bubbling geometries
- Infinite Distance Limits and Information Theory
- The landscape of complexity measures in 2D gravity
- Linear gravity from conformal symmetry
- Perturbative expansions of Rényi relative divergences and holography
- What kind of "complexity" is dual to holographic complexity?
- Purification Complexity without Purifications
- Circuit Complexity for Coherent-Thermal States in Bosonic String Theory