English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

According to 't Hooft, restoring Poincar\'e invariance in a holographiccellular automaton (CA) requires two distinct evolution laws that commute. Weexplore how this is realized in the AdS/CFT framework, assuming commutativityas a fundamental principle--much like general covariance once did--for encodingcurvature. In our setup, physical processes in a given spacetime are encoded ina CA; to preserve Poincar\'e symmetry, the spacetime curvature must effectivelyvanish, so we consider a near-extremal black D3-brane solution, in which boththe stretched horizon and the conformal boundary are approximated by Minkowskispace. AdS/CFT implies a spatial evolution law connecting these hypersurfaces.Commutativity means the final state does not depend on the order of timeevolution on each hypersurface and spatial evolution between them, forcing thetime evolution law on the horizon and boundary to coincide. To satisfy allthese conditions, we aim to demonstrate that the spatial evolution lawinevitably encapsulates the curvature of the bulk, including quantum effects.For a computational model, we compactify the hyperplanes to tori, reducing thedegrees of freedom to a finite number; taking these tori to infinite size thenrestores Poincar\'e symmetry. We propose a deep learning algorithm that, givena known time evolution law and commutativity, deduces the corresponding spatialevolution law.

Commutative Evolution Laws in Holographic Cellular Automata: AdS/CFT, Near-Extremal D3-Branes, and a Deep Learning Approach