Holographic Path-Integral Optimization

Understand

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.