Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$

Abstract

We construct a tessellation of AdS${}_3$, by extending the equilateral triangulation of AdS${}_2$ on the Poincaré disk based on the $(2,3,7)$ triangle group, suitable for studying strongly coupled phenomena and the AdS/CFT correspondence. A Hamiltonian form conducive to the study of dynamics and quantum computation is presented. We show agreement between lattice calculations and analytic results for the free scalar theory and find evidence of a second order critical transition for ${\varphi }^4$ theory using Monte Carlo simulations. Applications of this AdS Hamiltonian formulation to real time evolution and quantum computing are discussed.

arXiv comment20 pages, 5 figures

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Cited by in corpus (13)

• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• Simulating Holographic Conformal Field Theories on Hyperbolic Lattices
• Breitenlohner-Freedman bound on hyperbolic tilings
• Aperiodic spin chains at the boundary of hyperbolic tilings
• Topological linear response of hyperbolic Chern insulators
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Ising Model on the Affine Plane
• Holographic Foliations: Self-Similar Quasicrystals from Hyperbolic Honeycombs
• Wormhole-induced effective coupling in SYK chains
• Discrete JT gravity as an Ising model
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Fermions, quantum gravity and holography in two dimensions
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices