Bootstrap bounds on closed Einstein manifolds

Bonifacio, James; Hinterbichler, Kurt

doi:10.1007/jhep10(2020)069

Title: Bootstrap bounds on closed Einstein manifolds

Abstract

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.

Authors:

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

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

Publication Date:: Mon Oct 12 00:00:00 EDT 2020

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

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

OSTI Identifier:: 1852887

Grant/Contract Number:: SC0019143; 658908

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 10; Journal ID: ISSN 1029-8479

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; differential and algebraic geometry; classical theories of gravity; conformal field theory

Citation Formats


                    Bonifacio, James, and Hinterbichler, Kurt. Bootstrap bounds on closed Einstein manifolds.  United States: N. p., 2020. 
Web.  doi:10.1007/jhep10(2020)069.

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                    Bonifacio, James, & Hinterbichler, Kurt. Bootstrap bounds on closed Einstein manifolds.  United States.  https://doi.org/10.1007/jhep10(2020)069

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                    Bonifacio, James, and Hinterbichler, Kurt. Mon .  
"Bootstrap bounds on closed Einstein manifolds".  United States.  https://doi.org/10.1007/jhep10(2020)069.  https://www.osti.gov/servlets/purl/1852887.

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@article{osti_1852887,

  title        = {Bootstrap bounds on closed Einstein manifolds},

  author       = {Bonifacio, James and Hinterbichler, Kurt},

  abstractNote = {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.},

  doi          = {10.1007/jhep10(2020)069},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 10,

  volume       = 2020,

  place        = {United States},

  year         = {Mon Oct 12 00:00:00 EDT 2020},

  month        = {Mon Oct 12 00:00:00 EDT 2020}

}

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Works referencing / citing this record:

Eigenvalues and eigenforms on Calabi-Yau threefolds
preprint, January 2020

Ashmore, Anthony
arXiv
DOI: 10.48550/arxiv.2011.13929

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Similar Records

Title: Bootstrap bounds on closed Einstein manifolds

Abstract

Citation Formats

Sum rules for massive spin-2 Kaluza-Klein elastic scattering amplitudes journal, December 2019

Symmetric tensor spherical harmonics on the N ‐sphere and their application to the de Sitter group SO( N ,1) journal, July 1987

On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I journal, May 1978

Massive spin-2 scattering amplitudes in extra-dimensional theories journal, April 2020

The S-matrix bootstrap II: two dimensional amplitudes journal, November 2017

Bounding scalar operator dimensions in 4 D CFT journal, December 2008

The S-matrix bootstrap. Part III: higher dimensional amplitudes journal, December 2019

Scattering amplitudes of massive spin-2 Kaluza-Klein states grow only as O ( s ) journal, March 2020

Gravitational contribution to the Casimir energy in Kaluza-Klein theories journal, September 1984

Spherical harmonics and integral geometry on projective spaces journal, January 1983

Zeta functions and their asymptotic expansions for compact symmetric spaces of rank one journal, December 1976

Numerical Ricci-flat metrics on K3 journal, November 2005

On the stability of Riemannian manifold with parallel spinors journal, March 2005

Bohm and Einstein-Sasaki metrics, black holes, and cosmological event horizons journal, April 2003

Certain conditions for a Riemannian manifold to be isometric with a sphere journal, July 1962

Numerical Calabi–Yau metrics journal, March 2008

Eigenvalues and eigenfunctions of the scalar Laplace operator on Calabi-Yau manifolds journal, July 2008

Bootstraps to strings: solving random matrix models with positivity journal, June 2020

Propagateurs et commutateurs en relativité générale journal, January 1961

Kaluza-Klein towers on general manifolds journal, April 2014

Gravitational contribution to the Casimir energy in Kaluza-Klein theories journal, September 1984

Rigorous limits on the interaction strength in quantum field theory journal, April 2010

Eigenvalues and eigenforms on Calabi-Yau threefolds preprint, January 2020

Sum rules for massive spin-2 Kaluza-Klein elastic scattering amplitudes
journal, December 2019

Symmetric tensor spherical harmonics on the N ‐sphere and their application to the de Sitter group SO( N ,1)
journal, July 1987

On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
journal, May 1978

Massive spin-2 scattering amplitudes in extra-dimensional theories
journal, April 2020

The S-matrix bootstrap II: two dimensional amplitudes
journal, November 2017

Bounding scalar operator dimensions in 4 D CFT
journal, December 2008

The S-matrix bootstrap. Part III: higher dimensional amplitudes
journal, December 2019

Scattering amplitudes of massive spin-2 Kaluza-Klein states grow only as $O (s)$
journal, March 2020

Gravitational contribution to the Casimir energy in Kaluza-Klein theories
journal, September 1984

Spherical harmonics and integral geometry on projective spaces
journal, January 1983

Zeta functions and their asymptotic expansions for compact symmetric spaces of rank one
journal, December 1976

Numerical Ricci-flat metrics on K3
journal, November 2005

On the stability of Riemannian manifold with parallel spinors
journal, March 2005

Bohm and Einstein-Sasaki metrics, black holes, and cosmological event horizons
journal, April 2003

Certain conditions for a Riemannian manifold to be isometric with a sphere
journal, July 1962

Numerical Calabi–Yau metrics
journal, March 2008

Eigenvalues and eigenfunctions of the scalar Laplace operator on Calabi-Yau manifolds
journal, July 2008

Bootstraps to strings: solving random matrix models with positivity
journal, June 2020

Propagateurs et commutateurs en relativité générale
journal, January 1961

Kaluza-Klein towers on general manifolds
journal, April 2014

Gravitational contribution to the Casimir energy in Kaluza-Klein theories
journal, September 1984

Rigorous limits on the interaction strength in quantum field theory
journal, April 2010

Eigenvalues and eigenforms on Calabi-Yau threefolds
preprint, January 2020