The arithmetic geometry of AdS$_2$ and its continuum limit

Abstract : We present and study in detail the construction of a discrete and finite arithmetic geometry AdS$_2[N]$ and show that an appropriate scaling limit exists, as $N\to\infty,$ that can be identified with the universal AdS$_2$ radial and time near horizon geometry of extremal black holes. The AdS$_2[N]$ geometry has been proposed as a toy model for describing the nonlocal and chaotic dynamics of the horizon microscopic degrees of freedom, that carry the finite black hole entropy. In particular, it supports exact quantum mechanical bulk-boundary holography for single particle wave packet probes, that possess an $N-$dimensional Hilbert space of states. This costruction amounts, in fact, to a compression of the information about the continuous AdS$_2$ geometry and it provides an example of a framework for the study of quantum complexity of spacetime geometries.
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Contributor : Stam Nicolis <>
Submitted on : Tuesday, August 20, 2019 - 9:43:19 AM
Last modification on : Wednesday, August 21, 2019 - 1:22:40 AM

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  • HAL Id : hal-02267951, version 1
  • ARXIV : 1908.06641



Minos Axenides, Emmanuel Floratos, Stam Nicolis. The arithmetic geometry of AdS$_2$ and its continuum limit. 2019. ⟨hal-02267951⟩



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