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

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 functio...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Blommaert, Andreas, Mertens, Thomas G, Yao, Shunyu
Format: Article
Language:English
Subjects:
Boundary conditions
Correlation
Dilatons
Quantum gravity
Quantum mechanics
Wave functions
Online Access:Get full text
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Summary: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:2331-8422
DOI:10.48550/arxiv.2306.00941