离散JT重力作为Ising模型

IF 5.4 1区 物理与天体物理 Q1 Physics and Astronomy
Johanna Erdmenger, Jonathan Karl, Yanick Thurn, Matthias Vojta, Zhuo-Yu Xian
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引用次数: 0

摘要

受离散全息程序的启发,我们证明了欧几里得AdS2双曲平铺上的Jackiw-Teitelboim (JT)引力在受拓扑约束的对偶晶格上产生了一个Ising模型。伊辛模型包含一个渐近边界条件,其中自旋指向与磁场相反。拓扑约束在相反方向的自旋之间强制一个单一的域壁,具有圆形的拓扑结构。JT重力的解析与Ising模型的自由能有关,JT重力的经典极限对应于Ising低温极限。我们通过蒙特卡罗方法和平均场近似来研究这个Ising模型。对于无限双曲晶格的有限截断,两种理论之间的映射仅在区域壁具有有限大小的区域中有效。对于大正耦合或负耦合的极端情况,畴壁收缩为零或接触晶格边界。平均场分析证实了这种行为。我们期望我们的结果可以作为建立离散重力全息矩阵模型对偶性的起点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Discrete JT gravity as an Ising model

Inspired by the program of discrete holography, we show that Jackiw-Teitelboim (JT) gravity on a hyperbolic tiling of Euclidean AdS2 gives rise to an Ising model on the dual lattice, subject to a topological constraint. The Ising model involves an asymptotic boundary condition with spins pointing opposite to the magnetic field. The topological constraint enforces a single domain wall between the spins of opposite direction, with the topology of a circle. The resolvent of JT gravity is related to the free energy of this Ising model, and the classical limit of JT gravity corresponds to the Ising low-temperature limit. We study this Ising model through a Monte Carlo approach and a mean-field approximation. For finite truncations of the infinite hyperbolic lattice, the map between both theories is only valid in a regime in which the domain wall has a finite size. For the extremal cases of large positive or negative coupling, the domain wall either shrinks to zero or touches the boundary of the lattice. This behavior is confirmed by the mean-field analysis. We expect that our results may be used as a starting point for establishing a holographic matrix model duality for discretized gravity.

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来源期刊
Journal of High Energy Physics
Journal of High Energy Physics 物理-物理:粒子与场物理
CiteScore
10.30
自引率
46.30%
发文量
2107
审稿时长
1.5 months
期刊介绍: The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).
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