Dirichlet Scalar Determinants On Two-Dimensional Constant Curvature Disks
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912365076807680 |
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| author | Chaudhuri, Soumyadeep Ferrari, Frank |
| author_facet | Chaudhuri, Soumyadeep Ferrari, Frank |
| contents | We compute the scalar determinants $\det(Δ+M^{2})$ on the two-dimensional round disks of constant curvature $R=0$, $\mp 2$, for any finite boundary length $\ell$ and mass $M$, with Dirichlet boundary conditions, using the $ζ$-function prescription. When $M^{2}=\pm q(q+1)$, $q\in\mathbb N$, a simple expression involving only elementary functions and the Euler $Γ$ function is found. Applications to two-dimensional Liouville and Jackiw-Teitelboim quantum gravity are presented in a separate paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirichlet Scalar Determinants On Two-Dimensional Constant Curvature Disks Chaudhuri, Soumyadeep Ferrari, Frank High Energy Physics - Theory Mathematical Physics We compute the scalar determinants $\det(Δ+M^{2})$ on the two-dimensional round disks of constant curvature $R=0$, $\mp 2$, for any finite boundary length $\ell$ and mass $M$, with Dirichlet boundary conditions, using the $ζ$-function prescription. When $M^{2}=\pm q(q+1)$, $q\in\mathbb N$, a simple expression involving only elementary functions and the Euler $Γ$ function is found. Applications to two-dimensional Liouville and Jackiw-Teitelboim quantum gravity are presented in a separate paper. |
| title | Dirichlet Scalar Determinants On Two-Dimensional Constant Curvature Disks |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2405.14958 |