Quantum gravity of the Heisenberg algebra
Abstract 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 emerge...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2024)098 |
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| author | Ahmed Almheiri Akash Goel Xu-Yao Hu |
| author_facet | Ahmed Almheiri Akash Goel Xu-Yao Hu |
| author_sort | Ahmed Almheiri |
| collection | DOAJ |
| description | Abstract 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. |
| format | Article |
| id | doaj-art-6159fe5c052b4f608464ddd4a9eba3a4 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-6159fe5c052b4f608464ddd4a9eba3a42024-11-24T12:07:31ZengSpringerOpenJournal of High Energy Physics1029-84792024-08-012024814010.1007/JHEP08(2024)098Quantum gravity of the Heisenberg algebraAhmed Almheiri0Akash Goel1Xu-Yao Hu2New York University Abu DhabiCenter for Cosmology and Particle Physics, New York UniversityCenter for Cosmology and Particle Physics, New York UniversityAbstract 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.https://doi.org/10.1007/JHEP08(2024)0982D GravityField Theories in Lower DimensionsModels of Quantum GravityGauge-Gravity Correspondence |
| spellingShingle | Ahmed Almheiri Akash Goel Xu-Yao Hu Quantum gravity of the Heisenberg algebra Journal of High Energy Physics 2D Gravity Field Theories in Lower Dimensions Models of Quantum Gravity Gauge-Gravity Correspondence |
| title | Quantum gravity of the Heisenberg algebra |
| title_full | Quantum gravity of the Heisenberg algebra |
| title_fullStr | Quantum gravity of the Heisenberg algebra |
| title_full_unstemmed | Quantum gravity of the Heisenberg algebra |
| title_short | Quantum gravity of the Heisenberg algebra |
| title_sort | quantum gravity of the heisenberg algebra |
| topic | 2D Gravity Field Theories in Lower Dimensions Models of Quantum Gravity Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP08(2024)098 |
| work_keys_str_mv | AT ahmedalmheiri quantumgravityoftheheisenbergalgebra AT akashgoel quantumgravityoftheheisenbergalgebra AT xuyaohu quantumgravityoftheheisenbergalgebra |