论文标题
全息蜂窝自动机中的交换进化法：ADS/CFT，近超级D3烧烤和深度学习方法
Commutative Evolution Laws in Holographic Cellular Automata: AdS/CFT, Near-Extremal D3-Branes, and a Deep Learning Approach
论文作者
论文摘要
根据“ T Hooft”的说法，在全息细胞自动机（CA）中恢复Poincaré不变性需要两个截然不同的进化定律。我们探讨了在ADS/CFT框架中如何实现的，假设换击是一种基本原则 - 就像曾经的一般协方差一样 - 编码曲率。在我们的设置中，给定时空中的物理过程在CA中编码；为了保存庞加莱对称性，时空曲率必须有效消失，因此我们考虑了近乎超级黑的黑色D3-Brane溶液，其中伸展的地平线和形式的边界都被Minkowski空间近似。 AD/CFT意味着连接这些超曲面的空间进化定律。交换性意味着最终状态并不取决于每个超表面上的时间演变和它们之间的空间演化，从而迫使时间演化定律在地平线和边界上重合。为了满足所有这些条件，我们的目的是证明空间进化定律不可避免地封装了整体的曲率，包括量子效应。对于计算模型，我们将增压平面压缩到Tori，将自由度降低到有限的数字。将这些Tori带到无限的大小，然后恢复庞加莱对称性。我们提出了一种深度学习算法，鉴于已知的时间进化定律和换向，它可以推断出相应的空间进化定律。
According to 't Hooft, restoring Poincaré invariance in a holographic cellular automaton (CA) requires two distinct evolution laws that commute. We explore how this is realized in the AdS/CFT framework, assuming commutativity as a fundamental principle--much like general covariance once did--for encoding curvature. In our setup, physical processes in a given spacetime are encoded in a CA; to preserve Poincaré symmetry, the spacetime curvature must effectively vanish, so we consider a near-extremal black D3-brane solution, in which both the stretched horizon and the conformal boundary are approximated by Minkowski space. AdS/CFT implies a spatial evolution law connecting these hypersurfaces. Commutativity means the final state does not depend on the order of time evolution on each hypersurface and spatial evolution between them, forcing the time evolution law on the horizon and boundary to coincide. To satisfy all these conditions, we aim to demonstrate that the spatial evolution law inevitably encapsulates the curvature of the bulk, including quantum effects. For a computational model, we compactify the hyperplanes to tori, reducing the degrees of freedom to a finite number; taking these tori to infinite size then restores Poincaré symmetry. We propose a deep learning algorithm that, given a known time evolution law and commutativity, deduces the corresponding spatial evolution law.
