Path-Integral Optimization from Hartle-Hawking Wave Function
arXiv:2011.08188 · doi:10.1103/PhysRevD.103.046017
Abstract
We propose a gravity dual description of the path-integral optimization in conformal field theories arXiv:1703.00456, using Hartle-Hawking wave functions in anti-de Sitter spacetimes. We show that the maximization of the Hartle-Hawking wave function is equivalent to the path-integral optimization procedure. Namely, the variation of the wave function leads to a constraint, equivalent to the Neumann boundary condition on a bulk slice, whose classical solutions reproduce metrics from the path-integral optimization in conformal field theories. After taking the boundary limit of the semi-classical Hartle-Hawking wave function, we reproduce the path-integral complexity action in two dimensions as well as its higher and lower dimensional generalizations. We also discuss an emergence of holographic time from conformal field theory path-integrals.
7 pages, Revtex, 1 Figure, 1 Appendix, v2: Typos corrected, published version
References in corpus (44)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Comments on the Sachdev-Ye-Kitaev model
- A Covariant Holographic Entanglement Entropy Proposal
- Eternal Black Holes in AdS
- Entanglement renormalization
- Building up spacetime with quantum entanglement
- A class of quantum many-body states that can be efficiently simulated
- Complexity Equals Action
- Entanglement Renormalization and Holography
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Chaos in AdS holography
- Holographic Dual of BCFT
- Holographic duality from random tensor networks
- Aspects of AdS/BCFT
- Tensor Network Renormalization
- Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
- Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
- Entanglement renormalization for quantum fields
- Quantum Computation as Gravity
- Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
- Surface/State Correspondence as a Generalized Holography
- Einstein's Equations from Varying Complexity
- Path-Integral Complexity for Perturbed CFTs
- Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
- Tensor Networks from Kinematic Space
- Exact holographic mapping and emergent space-time geometry
- Complexity and the bulk volume, a new York time story
- Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
- Path integral optimization as circuit complexity
- Holographic Spacetimes as Quantum Circuits of Path-Integrations
- Holographic Entanglement of Purification from Conformal Field Theories
- Complexity measures from geometric actions on Virasoro and Kac-Moody orbits
- From Path Integrals to Tensor Networks for AdS/CFT
- Causal structure of the entanglement renormalization ansatz
- Geometric interpretation of the multi-scale entanglement renormalization ansatz
- Does Boundary Distinguish Complexities?
- Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
- Tensor network models of AdS/qCFT
- Holographic Tensor Networks in Full AdS/CFT
- Tensor networks as path integral geometry
- Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
- Building up spacetime with quantum entanglement II: It from BC-bit
Cited by in corpus (20)
- Holographic tensor network models and quantum error correction: A topical review
- BCFT and Islands in Two Dimensions
- Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
- Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
- Lorentzian threads as 'gatelines' and holographic complexity
- Quantum complexity in gravity, quantum field theory, and quantum information science
- Exact Gravity Duals for Simple Quantum Circuits
- Holographic Path-Integral Optimization
- Complexity=Anything: Singularity Probes
- Spacetime as a quantum circuit
- Emergent Einstein Equation in p-adic CFT Tensor Networks
- Building Tensor Networks for Holographic States
- Path Integral Complexity and Kasner singularities
- Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
- Q-curvature and Path Integral Complexity
- Circuit Complexity in
- Circuit complexity in proca theory
- Emergent dual holographic description as a non-perturbative generalization of the Wilsonian renormalization group
- Holographic and QFT Complexity with angular momentum
- Cost of holographic path integrals