Dynamical actions and q-representation theory for double-scaled SYK

A bstract We show that DSSYK amplitudes are reproduced by considering the quantum mechanics of a constrained particle on the quantum group SU q (1 , 1). We construct its left-and right-regular representations, and show that the representation matrices reproduce two-sided wavefunctions and correlatio...

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Bibliographic Details
Published in:The journal of high energy physics 2024-02, Vol.2024 (2), p.67-46, Article 67
Main Authors: Blommaert, Andreas, Mertens, Thomas G., Yao, Shunyu
Format: Article
Language:English
Subjects:
2D Gravity
Boundary conditions
Classical and Quantum Gravitation
Correlation
Decomposition
Dilatons
Elementary Particles
Field Theories in Lower Dimensions
Gravity
Non-Commutative Geometry
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum gravity
Quantum Groups
Quantum mechanics
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Wave functions
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Summary:A bstract We show that DSSYK amplitudes are reproduced by considering the quantum mechanics of a constrained particle on the quantum group SU q (1 , 1). We construct its left-and right-regular representations, and show that the representation matrices reproduce two-sided wavefunctions and correlation functions of DSSYK. We then construct a dynamical action and path integral for a particle on SU q (1 , 1), whose quantization reproduces the aforementioned representation theory. By imposing boundary conditions or constraining the system we find the q -analog of the Schwarzian and Liouville boundary path integral descriptions. This lays the technical groundwork for identifying the gravitational bulk description of DSSYK. We find evidence the theory in question is a sine dilaton gravity, which interestingly is capable of describing both AdS and dS quantum gravity.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP02(2024)067