Path-Integral Optimization from Hartle-Hawking Wave Function

TL;DR

This paper establishes a gravity dual for path-integral optimization in conformal field theories using Hartle-Hawking wave functions, linking wave function maximization to metric optimization and holographic time emergence.

Contribution

It introduces a gravity dual description of path-integral optimization via Hartle-Hawking wave functions, connecting boundary CFT procedures with bulk gravitational solutions.

Findings

Maximization of Hartle-Hawking wave function corresponds to path-integral optimization.

Classical solutions reproduce optimized metrics in conformal field theories.

Reproduction of path-integral complexity action in various dimensions.

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.