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.
Cite
@article{arxiv.2011.08188,
title = {Path-Integral Optimization from Hartle-Hawking Wave Function},
author = {Jan Boruch and Pawel Caputa and Tadashi Takayanagi},
journal= {arXiv preprint arXiv:2011.08188},
year = {2021}
}
Comments
7 pages, Revtex, 1 Figure, 1 Appendix, v2: Typos corrected, published version