dc.contributor.author Bonifacio, James dc.date.accessioned 2022-02-04T16:16:44Z dc.date.available 2022-02-04T16:16:44Z dc.date.issued 2022-02-03 dc.date.submitted 2021-09-28 dc.identifier.issn 1029-8479 dc.identifier.other jhep02(2022)025 dc.identifier.other 17710 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/333653 dc.description.abstract The 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 bound $\lambda_{i+1} \leq 1/2+3 \lambda_i+\sqrt{\lambda_i^2+2 \lambda_i+1/4}$ for 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. dc.language en dc.publisher Springer Science and Business Media LLC dc.subject Regular Article - Theoretical Physics dc.subject Differential and Algebraic Geometry dc.subject Conformal Field Theory dc.subject Field Theories in Higher Dimensions dc.title Bootstrap bounds on closed hyperbolic manifolds dc.type Article dc.date.updated 2022-02-04T16:16:43Z prism.issueIdentifier 2 prism.publicationName Journal of High Energy Physics prism.volume 2022 dc.identifier.doi 10.17863/CAM.81071 dcterms.dateAccepted 2022-01-16 rioxxterms.versionofrecord 10.1007/JHEP02(2022)025 rioxxterms.version VoR rioxxterms.licenseref.uri http://creativecommons.org/licenses/by/4.0/ dc.contributor.orcid Bonifacio, James [0000-0001-6633-7341] dc.identifier.eissn 1029-8479 dc.publisher.url http://dx.doi.org/10.1007/JHEP02(2022)025 cam.issuedOnline 2022-02-03 dc.identifier.arxiv 2107.09674
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