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Dirichlet Scalar Determinants On Two-Dimensional Constant Curvature Disks
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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.
Forward citations
Cited by 2 Pith papers
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Quantum Liouville Cosmology
Timelike Liouville disk path integrals in fixed K-representation produce Hartle-Hawking-like states, a conjecture for all-loop wavefunctions, and a K-independent inner product for 2D quantum cosmology.
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Neumann scalar determinants on constant curvature disks
Neumann determinants of the massive Laplacian on constant curvature disks are expressed as convergent infinite series, with exact special-mass reductions for m^2 = -η/L^2 q(q+1).
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