Bootstrapping closed hyperbolic surfaces


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Abstract

The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions and holomorphic s-differentials satisfy certain consistency conditions on closed hyperbolic surfaces. These consistency conditions can be derived by using spectral decompositions to write quadruple overlap integrals in terms of triple overlap integrals in different ways. We show how to efficiently construct these consistency conditions and use them to derive upper bounds on eigenvalues, following the approach of the conformal bootstrap. As an example of such a bootstrap bound, we find a numerical upper bound on the spectral gap of closed orientable hyperbolic surfaces that is nearly saturated by the Bolza surface.

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Keywords
Regular Article - Theoretical Physics, Differential and Algebraic Geometry, Scale and Conformal Symmetries
Journal Title
Journal of High Energy Physics
Conference Name
Journal ISSN
1029-8479
1029-8479
Volume Title
2022
Publisher
Springer Science and Business Media LLC