Bootstrap bounds on closed hyperbolic manifolds
Authors
Publication Date
2022-02-03Journal Title
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Volume
2022
Issue
2
Language
en
Type
Article
This Version
VoR
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Bonifacio, J. (2022). Bootstrap bounds on closed hyperbolic manifolds. Journal of High Energy Physics, 2022 (2) https://doi.org/10.1007/jhep02(2022)025
Abstract
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 λi+1 ≤ 1/2 + 3λi + λi2+2λi+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.
Keywords
Regular Article - Theoretical Physics, Differential and Algebraic Geometry, Conformal Field Theory, Field Theories in Higher Dimensions
Identifiers
jhep02(2022)025, 17710
External DOI: https://doi.org/10.1007/jhep02(2022)025
This record's URL: https://www.repository.cam.ac.uk/handle/1810/337555
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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