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arXiv · 2104.00010

Holographic Path-Integral Optimization

Jan Boruch·Pawel Caputa·Dongsheng Ge·Tadashi Takayanagi
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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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Jan Boruch, Pawel Caputa, Dongsheng Ge, Tadashi Takayanagi. 2021-03-31. Holographic Path-Integral Optimization. https://doi.org/10.1007/jhep07(2021)016

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