Bootstrap bounds on closed hyperbolic manifolds
Authors
Publication Date
2022Journal Title
Journal of High Energy Physics
ISSN
1029-8479
Publisher
Springer Science and Business Media LLC
Volume
2022
Issue
2
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
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
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.
Keywords
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/
Statistics
Total file downloads (since January 2020). For more information on metrics see the
IRUS guide.
Recommended or similar items
The current recommendation prototype on the Apollo Repository will be turned off on 03 February 2023. Although the pilot has been fruitful for both parties, the service provider IKVA is focusing on horizon scanning products and so the recommender service can no longer be supported. We recognise the importance of recommender services in supporting research discovery and are evaluating offerings from other service providers. If you would like to offer feedback on this decision please contact us on: support@repository.cam.ac.uk