Path-Integral Optimization from Hartle-Hawking Wave Function

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 (8)

• A class of quantum many-body states that can be efficiently simulated
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Surface/State Correspondence as a Generalized Holography
• Einstein's Equations from Varying Complexity
• Path integral optimization as circuit complexity
• Holographic Entanglement of Purification from Conformal Field Theories
• From Path Integrals to Tensor Networks for AdS/CFT
• Holographic Tensor Networks in Full AdS/CFT