Holographic Path-Integral Optimization

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.

arXiv comment74 pages, 6 figures, v2 References added, Published version

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• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
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• Quantum Information in Holographic Duality
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
• Lorentzian threads as 'gatelines' and holographic complexity
• Holographic Complexity in dS${}_{d+1}$
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Exact Gravity Duals for Simple Quantum Circuits
• Complexity=Anything: Singularity Probes
• Action complexity in the presence of defects and boundaries
• Path Integral Complexity and Kasner singularities
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• Q-curvature and Path Integral Complexity
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• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Holographic and QFT Complexity with angular momentum
• Cost of holographic path integrals