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dc.contributor.authorBonifacio, James
dc.date.accessioned2022-02-04T16:16:44Z
dc.date.available2022-02-04T16:16:44Z
dc.date.issued2022-02-03
dc.date.submitted2021-09-28
dc.identifier.issn1029-8479
dc.identifier.otherjhep02(2022)025
dc.identifier.other17710
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/333653
dc.description.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 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.languageen
dc.publisherSpringer Science and Business Media LLC
dc.subjectRegular Article - Theoretical Physics
dc.subjectDifferential and Algebraic Geometry
dc.subjectConformal Field Theory
dc.subjectField Theories in Higher Dimensions
dc.titleBootstrap bounds on closed hyperbolic manifolds
dc.typeArticle
dc.date.updated2022-02-04T16:16:43Z
prism.issueIdentifier2
prism.publicationNameJournal of High Energy Physics
prism.volume2022
dc.identifier.doi10.17863/CAM.81071
dcterms.dateAccepted2022-01-16
rioxxterms.versionofrecord10.1007/JHEP02(2022)025
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidBonifacio, James [0000-0001-6633-7341]
dc.identifier.eissn1029-8479
dc.publisher.urlhttp://dx.doi.org/10.1007/JHEP02(2022)025
cam.issuedOnline2022-02-03
dc.identifier.arxiv2107.09674


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