Quantum Liouville Cosmology
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914465534967808 |
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| author | Anninos, Dionysios Hertog, Thomas Karlsson, Joel |
| author_facet | Anninos, Dionysios Hertog, Thomas Karlsson, Joel |
| contents | We provide a detailed analysis of the disk path integral of timelike Liouville theory, conceived as a tractable and precise toy-model quantum cosmology in two dimensions. Disk path integrals with the insertion of matter field operators, taken along a judiciously chosen complex contour, yield states akin to the Hartle-Hawking wavefunction. Working in the fixed $K$-representation, where $K$ is the trace of the extrinsic curvature, we compute the one-loop wavefunctions and put forward a conjecture for the all-loop expressions. A suitable pairing of Liouville disk path integrals yields a $K$-independent quantity that may form the basis for a well-defined inner product on the space of Euclidean histories. We also consider other ensembles, including one with fixed area, and provide a static patch perspective with a timelike feature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Liouville Cosmology Anninos, Dionysios Hertog, Thomas Karlsson, Joel High Energy Physics - Theory General Relativity and Quantum Cosmology We provide a detailed analysis of the disk path integral of timelike Liouville theory, conceived as a tractable and precise toy-model quantum cosmology in two dimensions. Disk path integrals with the insertion of matter field operators, taken along a judiciously chosen complex contour, yield states akin to the Hartle-Hawking wavefunction. Working in the fixed $K$-representation, where $K$ is the trace of the extrinsic curvature, we compute the one-loop wavefunctions and put forward a conjecture for the all-loop expressions. A suitable pairing of Liouville disk path integrals yields a $K$-independent quantity that may form the basis for a well-defined inner product on the space of Euclidean histories. We also consider other ensembles, including one with fixed area, and provide a static patch perspective with a timelike feature. |
| title | Quantum Liouville Cosmology |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.15969 |