Holographic Path-Integral Optimization

• URL: http://arxiv.org/abs/2104.00010v2
• Date: Sat, 24 Jul 2021 17:59:59 GMT
• Title: Holographic Path-Integral Optimization
• Authors: Jan Boruch, Pawel Caputa, Dongsheng Ge, Tadashi Takayanagi
• Abstract summary: We show that metrics that maximize gravity wave functions in holographic geometries precisely match those in the path-integral optimization procedure for their dual CFT states. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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