A Cordial Introduction to Double Scaled SYK
Micha Berkooz, Ohad Mamroud

TL;DR
This paper reviews the double scaled SYK model, highlighting its exact solvable properties, algebraic structures, and connections to quantum gravity, offering insights into non-commutative geometries and universality classes.
Contribution
It provides a comprehensive overview of the double scaled SYK model, including exact solutions, algebraic frameworks, and links to quantum gravity and non-commutative spaces.
Findings
Exact spectrum and correlation functions derived
Connection to Schwarzian quantum mechanics established
Quantum group structure suggests non-commutative $AdS_2$ geometry
Abstract
We review recent progress regarding the double scaled Sachdev-Ye-Kitaev model and other -local quantum mechanical random Hamiltonians. These models exhibit an expansion using chord diagrams, which can be solved by combinatorial methods. We describe exact results in these models, including their spectrum, correlation functions, and Lyapunov exponent. In a certain limit, these techniques manifest the relation to the Schwarzian quantum mechanics, a theory of quantum gravity in . More generally, the theory is controlled by a rigid algebraic structure of a quantum group, suggesting a theory of quantum gravity on non-commutative -deformed . We conclude with discussion of related universality classes, and survey some of the current research directions.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Black Holes and Theoretical Physics · Algebraic structures and combinatorial models
