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arXiv · 2405.14958

Dirichlet Scalar Determinants On Two-Dimensional Constant Curvature Disks

Soumyadeep Chaudhuri·Frank Ferrari
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Abstract

We compute the scalar determinants $\det(\Delta+M^{2})$ 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 $\zeta$-function prescription. When $M^{2}=\pm q(q+1)$, $q\in\mathbb N$, a simple expression involving only elementary functions and the Euler $\Gamma$ function is found. Applications to two-dimensional Liouville and Jackiw-Teitelboim quantum gravity are presented in a separate paper.

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Soumyadeep Chaudhuri, Frank Ferrari. 2024-05-23. Dirichlet Scalar Determinants On Two-Dimensional Constant Curvature Disks. https://doi.org/10.1007/s00023-025-01576-w

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