Bootstrapping Closed Hyperbolic Surfaces

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.

20 pages; v2: minor changes

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Cited by in corpus (10)

• Bootstrapping the 3d Ising Stress Tensor
• Almost all extremal black holes in AdS are singular
• New Developments in the Numerical Conformal Bootstrap
• Selberg trace formula in hyperbolic band theory
• Bootstrapping closed string field theory
• Casimir Energy and Modularity in Higher-dimensional Conformal Field Theories
• Hyperbolic string tadpole
• On the hyperbolic Bloch transform
• From Noncommutative Geometry to Random Matrix Theory
• Automorphic Spectra and the Conformal Bootstrap