The spectrum of pure dS$_3$ gravity in the static patch
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| Format: | Preprint |
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2025
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| author | Chakravarty, Joydeep Maloney, Alexander Namjou, Keivan Ross, Simon F. |
| author_facet | Chakravarty, Joydeep Maloney, Alexander Namjou, Keivan Ross, Simon F. |
| contents | We consider the quantum mechanical description of the de Sitter static patch in three-dimensional general relativity. We consider a Lorentzian path integral that conjecturally computes the Fourier transform of the spectrum of the static patch Hamiltonian. We regulate a saddle point for this integral by a complex deformation that connects it to future infinity. Our computation is thus closely connected with the wave function of de Sitter gravity on a torus at future infinity. Motivated by this, we identify an infinite number of saddle points that contribute to our Lorentzian path integral. Their sum gives a surprisingly simple result, which agrees with the expected features of the de Sitter static patch. For example, the thermal entropy, evaluated at the de Sitter temperature, agrees with the Bekenstein-Hawking formula. We also obtain a spectrum in the spin-zero sector, which is bounded, discrete, and has an integer degeneracy of states. It includes a dense spectrum of states, making both positive and negative contributions to the trace, arranged in such a way that negative contributions are invisible in the computation of any smooth observable. Nevertheless, several mysteries remain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_06420 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The spectrum of pure dS$_3$ gravity in the static patch Chakravarty, Joydeep Maloney, Alexander Namjou, Keivan Ross, Simon F. High Energy Physics - Theory General Relativity and Quantum Cosmology We consider the quantum mechanical description of the de Sitter static patch in three-dimensional general relativity. We consider a Lorentzian path integral that conjecturally computes the Fourier transform of the spectrum of the static patch Hamiltonian. We regulate a saddle point for this integral by a complex deformation that connects it to future infinity. Our computation is thus closely connected with the wave function of de Sitter gravity on a torus at future infinity. Motivated by this, we identify an infinite number of saddle points that contribute to our Lorentzian path integral. Their sum gives a surprisingly simple result, which agrees with the expected features of the de Sitter static patch. For example, the thermal entropy, evaluated at the de Sitter temperature, agrees with the Bekenstein-Hawking formula. We also obtain a spectrum in the spin-zero sector, which is bounded, discrete, and has an integer degeneracy of states. It includes a dense spectrum of states, making both positive and negative contributions to the trace, arranged in such a way that negative contributions are invisible in the computation of any smooth observable. Nevertheless, several mysteries remain. |
| title | The spectrum of pure dS$_3$ gravity in the static patch |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.06420 |