Bootstrap bounds on closed Einstein manifolds

Bonifacio, James; Hinterbichler, Kurt

doi:10.1007/jhep10(2020)069

Bootstrap bounds on closed Einstein manifolds

Journal Article · Mon Oct 12 00:00:00 EDT 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep10(2020)069· OSTI ID:1852887

Bonifacio, James ^[1]; Hinterbichler, Kurt ^[2]

Case Western Reserve Univ., Cleveland, OH (United States); Case Western Reserve Univ., Cleveland, OH (United States)
Case Western Reserve Univ., Cleveland, OH (United States)

A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

View Accepted Manuscript (DOE)

Research Organization:: Case Western Reserve Univ., Cleveland, OH (United States)

Sponsoring Organization:: Simons Foundation; USDOE Office of Science (SC)

Grant/Contract Number:: SC0019143

OSTI ID:: 1852887

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2020; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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GENERAL PHYSICS
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