Quantum gravity of the Heisenberg algebra

A bstract We consider a simplified model of double scaled SYK (DSSYK) in which the Hamiltonian is the position operator of the Harmonic oscillator. This model captures the high temperature limit of DSSYK but could also be defined as a quantum theory in its own right. We study properties of the emerg...

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Bibliographic Details
Published in:The journal of high energy physics 2024-08, Vol.2024 (8), p.98-40, Article 98
Main Authors: Almheiri, Ahmed, Goel, Akash, Hu, Xu-Yao
Format: Article
Language:English
Subjects:
2D Gravity
Algebra
Approximation
Classical and Quantum Gravitation
Correlation
Dilatons
Elementary Particles
Field Theories in Lower Dimensions
Functionals
Gauge-Gravity Correspondence
Geometry
Gravity
Hamiltonian functions
Harmonic oscillators
High temperature
Hilbert space
Models of Quantum Gravity
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum gravity
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
Spacetime
String Theory
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Summary:A bstract We consider a simplified model of double scaled SYK (DSSYK) in which the Hamiltonian is the position operator of the Harmonic oscillator. This model captures the high temperature limit of DSSYK but could also be defined as a quantum theory in its own right. We study properties of the emergent geometry including its dynamics in response to inserting matter particles. In particular, we find that the model displays de Sitter-like properties such as that infalling matter reduces the rate of growth of geodesic slices between the two boundaries. The simplicity of the model allows us to compute the full generating functional for correlation functions of the length mode or any number of matter operators. We provide evidence that the effective action of the geodesic length between boundary points is non-local. Furthermore, we use the on-shell solution for the geodesic lengths between any two boundary points to reconstruct an effective bulk metric and reverse engineer the dilaton gravity theory that generates this metric as a solution.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP08(2024)098