论文标题
广告模块化离散化的连续限制$ _2 $
The continuum limit of the modular discretization of AdS$_2$
论文作者
论文摘要
根据“ T Hooft and Susskind的全息图”，黑洞熵，$ s _ {\ rm BH} $，由混乱的微观自由度携带，它们生活在近地平线几何形状，并具有有限尺寸的Hilbert空间，$ d = \ exp（$ d = \ exp（s s _ p）在以前的工作中，我们提出，近地平线几何形状可以通过离散，有限的，随机的几何形状来描述，可以解释自由度的自由度，ads $ _2 [\ mathbb {z} _n] $，其中$ n $与$ s _ $ s_ _ {\ rm bh} $。作为一个空旷的问题，仍然是如何在n到达无穷大时恢复光滑的ADS2几何形状的方式。在这项贡献中，我们介绍了解决此问题的显着点，其中涉及将ADS $ _2 [\ MATHBB {Z} _n] $嵌入有限的几何形状家族中，ADS $ _2^m [\ MATHBB {Z} _n] $，其中$ M $是另一个Integer，是另一个Integer，在2+1 Minkowsski ins of 2+1 minkostki offere。在这种建筑中，$ n $和$ m $可以视为IR和UV截止。使用fibonacci和$ k $ -fibonAcci序列的属性，以相关的方式将$ n $和$ m $与无限的方式相关的方式来获得相当于平滑广告$ _2 $几何形状的连续限制。此方法也可以直接应用于高维广告的空间。
According to the holographic picture of 't Hooft and Susskind, the black hole entropy, $S_{\rm BH}$, is carried by the chaotic microscopic degrees of freedom, that live in the near horizon geometry and have a Hilbert space of states of finite dimension, $d=\exp(S_{\rm BH})$. In previous work we have proposed that the near horizon geometry, when the microscopic degrees of freedom can be resolved, can be described by the discrete, finite, random geometry, AdS$_2[\mathbb{Z}_N]$, where $N$ is proportional to $S_{\rm BH}$. What had remained as an open problem was how the smooth AdS2 geometry can be recovered, in the limit when N goes to infinity. In this contribution we present the salient points of the solution to this problem, which involves embedding AdS$_2[\mathbb{Z}_N]$ in a family of finite geometries, AdS$_2^M[\mathbb{Z}_N]$, where $M$ is another integer, within 2+1 Minkowski spacetime. In this construction $N$ and $M$ can be considered IR and UV cutoffs. The continuum limit, corresponding to the smooth AdS$_2$ geometry, is obtained by taking $N$ and $M$ to infinity in a correlated way, using properties of the Fibonacci and $k$-Fibonacci sequences. This method can be directly applied to higher-dimensional AdS spacetimes, also.
