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arXiv 1306.5670hep-th
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AdS2/CFT1全息图的模离散化

Modular discretization of the AdS2/CFT1 Holography

M. Axenides, E. G. Floratos, S. Nicolis

备注：
33 pages LaTeX2e, 1 JPEG figure. Typos corrected, references added. Clarification of several points in the abstract and the text
发表信息：
JHEP 1402 (2014) 109
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摘要：

我们提出了一个有限的离散化的黑洞的几何和动力学。我们实现了我们的建议，在极端黑洞的情况下，其径向和时间近视界几何是已知的AdS $_2=SL(2,\mathbb{R})/SO(1,1,\mathbb{R})$。我们实现了它的离散化，取代了一组实数$\mathbb{R}$与整数模$N$，与AdS $_2$去到有限几何AdS $_2[N]=SL(2,\mathbb{Z}_N)/SO(1,1,\mathbb{Z}_N)$。我们用广义Arnol'd猫映射${\sf A}\in SL(2,\mathbb{Z}_N)$来模拟微观自由度的动力学，该映射是经典和量子水平上的几何等距。它们表现出强算术混沌、动力学熵、非定域性和截断离散$N$因子分解等特性，这些特性对快速量子信息处理至关重要.最后，我们构造了一种新的么正全息对应，AdS $_2[N]$ /CFT $_1[N]$，通过体几何和边界几何的相干态。

英文摘要：

We propose a finite discretization for the black hole geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS$_2=SL(2,\mathbb{R})/SO(1,1,\mathbb{R})$. We implement its discretization by replacing the set of real numbers $\mathbb{R}$ with the set of integers modulo $N$, with AdS$_2$ going over to the finite geometry AdS$_2[N]=SL(2,\mathbb{Z}_N)/SO(1,1,\mathbb{Z}_N)$. We model the dynamics of the microscopic degrees of freedom by generalized Arnol'd cat maps, ${\sf A}\in SL(2,\mathbb{Z}_N)$, which are isometries of the geometry at both the classical and quantum levels. These exhibit well studied properties of strong arithmetic chaos, dynamical entropy, nonlocality and factorization in the cutoff discretization $N$, which are crucial for fast quantum information processing. We construct, finally, a new kind of unitary and holographic correspondence, for AdS$_2[N]$/CFT$_1[N]$, via coherent states of both the bulk and boundary geometries.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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