Dynamical actions and q-representation theory for double-scaled SYK
Abstract 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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2024)067 |
| _version_ | 1797276145071161344 |
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| author | Andreas Blommaert Thomas G. Mertens Shunyu Yao |
| author_facet | Andreas Blommaert Thomas G. Mertens Shunyu Yao |
| author_sort | Andreas Blommaert |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-03-07T15:24:07Z |
| format | Article |
| id | doaj.art-acbf0e32d1c640b386a0c51439514c2c |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-07T15:24:07Z |
| publishDate | 2024-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-acbf0e32d1c640b386a0c51439514c2c2024-03-05T17:27:50ZengSpringerOpenJournal of High Energy Physics1029-84792024-02-012024214610.1007/JHEP02(2024)067Dynamical actions and q-representation theory for double-scaled SYKAndreas Blommaert0Thomas G. Mertens1Shunyu Yao2SISSA and INFNDepartment of Physics and Astronomy, Ghent UniversityDepartment of Physics, Stanford UniversityAbstract 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.https://doi.org/10.1007/JHEP02(2024)0672D GravityQuantum GroupsField Theories in Lower DimensionsNon-Commutative Geometry |
| spellingShingle | Andreas Blommaert Thomas G. Mertens Shunyu Yao Dynamical actions and q-representation theory for double-scaled SYK Journal of High Energy Physics 2D Gravity Quantum Groups Field Theories in Lower Dimensions Non-Commutative Geometry |
| title | Dynamical actions and q-representation theory for double-scaled SYK |
| title_full | Dynamical actions and q-representation theory for double-scaled SYK |
| title_fullStr | Dynamical actions and q-representation theory for double-scaled SYK |
| title_full_unstemmed | Dynamical actions and q-representation theory for double-scaled SYK |
| title_short | Dynamical actions and q-representation theory for double-scaled SYK |
| title_sort | dynamical actions and q representation theory for double scaled syk |
| topic | 2D Gravity Quantum Groups Field Theories in Lower Dimensions Non-Commutative Geometry |
| url | https://doi.org/10.1007/JHEP02(2024)067 |
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