Phase transitions and uberholography of holographic pure-state geometries

• URL: http://arxiv.org/abs/2607.06870v1
• Date: Wed, 08 Jul 2026 00:01:53 GMT
• Title: Phase transitions and uberholography of holographic pure-state geometries
• Abstract summary: We study the error-correcting properties of pure-state holographic geometries in which mixed boundary subregions are replaced.<n>We show that the hole-punching uberholography cannot start within an RT-boundary, while an untouched boundary can still fractalize.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the error-correcting properties of pure-state holographic geometries, in which mixed boundary subregions are replaced, via the surface/state correspondence, by the Ryu--Takayanagi (RT) geodesic bounding their entanglement wedges. In AdS$_3$/CFT$_2$ we derive a cross-ratio threshold relation $η'/η= e^{ΔH/2}$ for the connected/disconnected transition of the entanglement wedge when two holes are punched in such a geometry. The quantity $ΔH$ is sourced entirely by geodesics ending on RT boundaries. It shifts the standard two-interval threshold $η= 1/2$, and we classify when its sign is fixed by the pattern of hole endpoints. Turning to code properties, we show that the recursive hole-punching underlying uberholography cannot start within an RT-boundary, while an untouched asymptotic boundary can still fractalize, and we find numerically that in the configurations we study it does so with the universal fractal dimension $α\approx 0.786$. The resulting upper bounds on price and distance are nevertheless procedure dependent. In the configurations we study, punching holes on the asymptotic boundary while retaining the RT-boundary yields strictly tighter bounds than first tracing out the RT-boundary and then fractalizing.

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