Open-Channel Operator Closure of the Finite-Cutoff JT Gravity Disk Amplitude
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910123246485504 |
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| author | Zhou, Ye |
| author_facet | Zhou, Ye |
| contents | The finite-cutoff disk amplitude of Jackiw-Teitelboim (JT) gravity is known from closed-channel spectral methods and finite-cutoff trumpet/cap gluing, while its complete open-channel operator formulation has remained incomplete. In this paper, we provide an operator-level open-channel closure of this known result. More precisely, we separate the data imported from finite-cutoff geometry -- the rigid length --momentum kernel, the disk-trumpet gluing relation, and hence the target cap overlap -- from the structures derived within the parity-even auxiliary problem, namely the Neumann vacuum sector, the generalized eigenbasis, and the branch-projecting spectral functional. When these ingredients are combined, the known finite-cutoff disk amplitude is reproduced as a boundary-state matrix element. We further show that the induced finite-cutoff geodesic sector is bandlimited and therefore admits sampled and branch-doubled discrete representations of the same physical sector, rather than an independent microscopic lattice model. Finally, we show that the resulting compact-support branch-difference amplitude is not the ordinary thermal trace of any single lower-bounded self-adjoint $β$-independent Hamiltonian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10977 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Open-Channel Operator Closure of the Finite-Cutoff JT Gravity Disk Amplitude Zhou, Ye General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics The finite-cutoff disk amplitude of Jackiw-Teitelboim (JT) gravity is known from closed-channel spectral methods and finite-cutoff trumpet/cap gluing, while its complete open-channel operator formulation has remained incomplete. In this paper, we provide an operator-level open-channel closure of this known result. More precisely, we separate the data imported from finite-cutoff geometry -- the rigid length --momentum kernel, the disk-trumpet gluing relation, and hence the target cap overlap -- from the structures derived within the parity-even auxiliary problem, namely the Neumann vacuum sector, the generalized eigenbasis, and the branch-projecting spectral functional. When these ingredients are combined, the known finite-cutoff disk amplitude is reproduced as a boundary-state matrix element. We further show that the induced finite-cutoff geodesic sector is bandlimited and therefore admits sampled and branch-doubled discrete representations of the same physical sector, rather than an independent microscopic lattice model. Finally, we show that the resulting compact-support branch-difference amplitude is not the ordinary thermal trace of any single lower-bounded self-adjoint $β$-independent Hamiltonian. |
| title | Open-Channel Operator Closure of the Finite-Cutoff JT Gravity Disk Amplitude |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.10977 |