Holographic Path-Integral Optimization

TL;DR

This paper explores the holographic dual of path-integral optimization in conformal field theories by relating it to maximization of Hartle-Hawking wave functions in AdS spacetimes, extending the framework to excited states and Lorentzian geometries.

Contribution

It establishes a holographic interpretation of path-integral optimization via Hartle-Hawking wave functions, including new analyses of excited states and Lorentzian geometries.

Findings

Metrics maximizing gravity wave functions match those from CFT path-integral optimization.

Analysis of excited states in various dimensions, including JT gravity.

Extension to Lorentzian AdS and de Sitter geometries.

Abstract

In this work we elaborate on holographic description of the path-integral optimization in conformal field theories (CFT) using Hartle-Hawking wave functions in Anti-de Sitter spacetimes. We argue that the maximization of the Hartle-Hawking wave function is equivalent to the path-integral optimization procedure in CFT. In particular, we show that metrics that maximize gravity wave functions computed in particular holographic geometries, precisely match those derived in the path-integral optimization procedure for their dual CFT states. The present work is a detailed version of \cite{Boruch:2020wax} and contains many new results such as analysis of excited states in various dimensions including JT gravity, and a new way of estimating holographic path-integral complexity from Hartle-Hawking wave functions. Finally, we generalize the analysis to Lorentzian Anti-de Sitter and de Sitter geometries and use it to shed light on path-integral optimization in Lorentzian CFTs.