Path-Integral Optimization from Hartle-Hawking Wave Function

• URL: http://arxiv.org/abs/2011.08188v2
• Date: Sun, 4 Apr 2021 14:29:27 GMT
• Title: Path-Integral Optimization from Hartle-Hawking Wave Function
• Authors: Jan Boruch, Pawel Caputa, Tadashi Takayanagi
• Abstract summary: We show that the variation of the wave function leads to a constraint, equivalent to the Neumann boundary condition on a bulk slice. We reproduce the path-integral complexity action in two dimensions as well as its higher and lower dimensional generalizations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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