Abstract
AbstractThe eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions must satisfy certain consistency conditions on compact Riemannian manifolds. These consistency conditions are derived by using spectral decompositions to write quadruple overlap integrals in terms of products of triple overlap integrals in multiple ways. In this paper, we show how these consistency conditions imply bounds on the Laplacian eigenvalues and triple overlap integrals of closed hyperbolic manifolds, in analogy to the conformal bootstrap bounds on conformal field theories. We find an upper bound on the gap between two consecutive nonzero eigenvalues of the Laplace-Beltrami operator in terms of the smaller eigenvalue, an upper bound on the smallest eigenvalue of the rough Laplacian on symmetric, transverse-traceless, rank-2 tensors, and bounds on integrals of products of eigenfunctions and eigentensors. Our strongest bounds involve numerically solving semidefinite programs and are presented as exclusion plots. We also prove the analytic boundλi+1≤ 1/2 + 3λi+$$ \sqrt{\lambda_i^2+2{\lambda}_i+1/4} $$λi2+2λi+1/4for consecutive nonzero eigenvalues of the Laplace-Beltrami operator on closed orientable hyperbolic surfaces. We give examples of genus-2 surfaces that nearly saturate some of these bounds. To derive the consistency conditions, we make use of a transverse-traceless decomposition for symmetric tensors of arbitrary rank.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Uniqueness of the extremal Schwarzschild de Sitter spacetime;Letters in Mathematical Physics;2024-01-18
2. Automorphic spectra and the conformal bootstrap;Communications of the American Mathematical Society;2024-01-17
3. Bootstrapping closed hyperbolic surfaces;Journal of High Energy Physics;2022-03