Holographic path-integral optimization

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