Unitarization from geometry

Bonifacio, James; Hinterbichler, Kurt

doi:10.1007/jhep12(2019)165

Unitarization from geometry

Journal Article · Mon Dec 30 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep12(2019)165· OSTI ID:1803591

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

Case Western Reserve Univ., Cleveland, OH (United States). Dept. of Physics. CERCA; OSTI
Case Western Reserve Univ., Cleveland, OH (United States). Dept. of Physics. CERCA

We study the perturbative unitarity of scattering amplitudes in general dimensional reductions of Yang–Mills theories and general relativity on closed internal manifolds. For the tree amplitudes of the dimensionally reduced theory to have the expected high-energy behavior of the higher-dimensional theory, the masses and cubic couplings of the Kaluza–Klein states must satisfy certain sum rules that ensure there are nontrivial cancellations between Feynman diagrams. These sum rules give constraints on the spectra and triple overlap integrals of eigenfunctions of Laplacian operators on the internal manifold and can be proven directly using Hodge and eigenfunction decompositions. One consequence of these constraints is that there is an upper bound on the ratio of consecutive eigenvalues of the scalar Laplacian on closed Ricci-flat manifolds with special holonomy. This gives a sharp bound on the allowed gaps between Kaluza–Klein excitations of the graviton that also applies to Calabi–Yau compactifications of string theory.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0019143

OSTI ID:: 1803591

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (71)

Propagateurs et commutateurs en relativité générale Lichnerowicz, André Publications mathématiques de l'IHÉS, Vol. 10, Issue 1 https://doi.org/10.1007/bf02684612	journal	January 1961
Strong-coupling scales and the graph structure of multi-gravity theories Scargill, James H. C.; Noller, Johannes Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/jhep01(2016)029	journal	January 2016
Fast conformal bootstrap and constraints on 3d gravity Afkhami-Jeddi, Nima; Hartman, Thomas; Tajdini, Amirhossein Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/jhep05(2019)087	journal	May 2019
Non-geometric backgrounds in string theory Plauschinn, Erik Physics Reports, Vol. 798 https://doi.org/10.1016/j.physrep.2018.12.002	journal	March 2019
Eigenvalues of the Laplace Operator on Certain Manifolds Milnor, J. Proceedings of the National Academy of Sciences, Vol. 51, Issue 4 https://doi.org/10.1073/pnas.51.4.542	journal	April 1964
Bounds on amplitudes in effective theories with massive spinning particles Bonifacio, James; Hinterbichler, Kurt Physical Review D, Vol. 98, Issue 4 https://doi.org/10.1103/physrevd.98.045003	journal	August 2018
Kaluza–Klein reductions and AdS/Ricci-flat correspondence Caldarelli, Marco M.; Skenderis, Kostas The European Physical Journal C, Vol. 78, Issue 7 https://doi.org/10.1140/epjc/s10052-018-6058-8	journal	July 2018
Unitarity in Gauge Symmetry Breaking on an Orbifold Abe, Y.; Haba, N.; Higashide, Y. Progress of Theoretical Physics, Vol. 109, Issue 5 https://doi.org/10.1143/ptp.109.831	journal	May 2003
Certain conditions for a Riemannian manifold to be isometric with a sphere Obata, Morio Journal of the Mathematical Society of Japan, Vol. 14, Issue 3 https://doi.org/10.2969/jmsj/01430333	journal	July 1962
Kaluza-Klein Towers on General Manifolds Hinterbichler, Kurt; Levin, Janna; Zukowski, Claire arXiv https://doi.org/10.48550/arxiv.1310.6353	text	January 2013
On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I Yau, Shing-Tung Communications on Pure and Applied Mathematics, Vol. 31, Issue 3 https://doi.org/10.1002/cpa.3160310304	journal	May 1978
On the Ratio of Consecutive Eigenvalues Payne, L. E.; Pólya, G.; Weinberger, H. F. Journal of Mathematics and Physics, Vol. 35, Issue 1-4 https://doi.org/10.1002/sapm1956351289	journal	April 1956
Eigenvalue comparison theorems and its geometric applications Cheng, Shiu-Yuen Mathematische Zeitschrift, Vol. 143, Issue 3 https://doi.org/10.1007/BF01214381	journal	October 1975
Quantentheorie und f�nfdimensionale Relativit�tstheorie Klein, Oskar Zeitschrift f�r Physik, Vol. 37, Issue 12 https://doi.org/10.1007/BF01397481	journal	December 1926
Propagateurs et commutateurs en relativité générale Lichnerowicz, André Publications mathématiques de l'IHÉS, Vol. 10, Issue 1 https://doi.org/10.1007/BF02684612	journal	January 1961
Strong-coupling scales and the graph structure of multi-gravity theories Scargill, James H. C.; Noller, Johannes Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/JHEP01(2016)029	journal	January 2016
Bimetric gravity from ghost-free massive gravity Hassan, S. F.; Rosen, Rachel A. Journal of High Energy Physics, Vol. 2012, Issue 2 https://doi.org/10.1007/JHEP02(2012)126	journal	February 2012
Causality constraints on corrections to the graviton three-point coupling Camanho, Xián O.; Edelstein, José D.; Maldacena, Juan Journal of High Energy Physics, Vol. 2016, Issue 2 https://doi.org/10.1007/JHEP02(2016)020	journal	February 2016
Massive spin-2 scattering and asymptotic superluminality Hinterbichler, Kurt; Joyce, Austin; Rosen, Rachel A. Journal of High Energy Physics, Vol. 2018, Issue 3 https://doi.org/10.1007/JHEP03(2018)051	journal	March 2018
Positivity bounds for massive spin-1 and spin-2 fields de Rham, Claudia; Melville, Scott; Tolley, Andrew J. Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)182	journal	March 2019
A bound on massive higher spin particles Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein Journal of High Energy Physics, Vol. 2019, Issue 4 https://doi.org/10.1007/JHEP04(2019)056	journal	April 2019
Massive and massless spin-2 scattering and asymptotic superluminality Bonifacio, James; Hinterbichler, Kurt; Joyce, Austin Journal of High Energy Physics, Vol. 2018, Issue 6 https://doi.org/10.1007/JHEP06(2018)075	journal	June 2018
Interacting spin-2 fields Hinterbichler, Kurt; Rosen, Rachel A. Journal of High Energy Physics, Vol. 2012, Issue 7 https://doi.org/10.1007/JHEP07(2012)047	journal	July 2012
Strings from massive higher spins: the asymptotic uniqueness of the Veneziano amplitude Caron-Huot, Simon; Komargodski, Zohar; Sever, Amit Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)026	journal	October 2017
On the stability of Riemannian manifold with parallel spinors Dai, Xianzhe; Wang, Xiaodong; Wei, Guofang Inventiones mathematicae, Vol. 161, Issue 1 https://doi.org/10.1007/s00222-004-0424-x	journal	March 2005
Inhomogeneous Einstein metrics on low-dimensional spheres and other low-dimensional spaces Böhm, Christoph Inventiones Mathematicae, Vol. 134, Issue 1 https://doi.org/10.1007/s002220050261	journal	September 1998
Consistent interacting massive spin-2 requires an infinity of states Duff, M. J.; Pope, C. N.; Stelle, K. S. Physics Letters B, Vol. 223, Issue 3-4 https://doi.org/10.1016/0370-2693(89)91620-1	journal	June 1989
Effective field theory for massive gravitons and gravity in theory space Arkani-Hamed, Nima; Georgi, Howard; Schwartz, Matthew D. Annals of Physics, Vol. 305, Issue 2 https://doi.org/10.1016/S0003-4916(03)00068-X	journal	June 2003
Unitarity of compactified five-dimensional Yang–Mills theory Chivukula, R. Sekhar; Dicus, Duane A.; He, H. -J. Physics Letters B, Vol. 525, Issue 1-2 https://doi.org/10.1016/S0370-2693(01)01435-6	journal	January 2002
Unitarity of deconstructed five-dimensional Yang–Mills theory Chivukula, R. Sekhar; He, Hong-Jian Physics Letters B, Vol. 532, Issue 1-2 https://doi.org/10.1016/S0370-2693(02)01495-8	journal	April 2002
Numerical Calabi–Yau metrics Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio Journal of Mathematical Physics, Vol. 49, Issue 3 https://doi.org/10.1063/1.2888403	journal	March 2008
Symmetric tensor spherical harmonics on the N ‐sphere and their application to the de Sitter group SO( N ,1) Higuchi, Atsushi Journal of Mathematical Physics, Vol. 28, Issue 7 https://doi.org/10.1063/1.527513	journal	July 1987
Massive gravity Vainshtein, A. Surveys in High Energy Physics, Vol. 20, Issue 1-4 https://doi.org/10.1080/01422410500314199	journal	January 2006
Dynamics in non-globally-hyperbolic static spacetimes: III. Anti-de Sitter spacetime Ishibashi, Akihiro; Wald, Robert M. Classical and Quantum Gravity, Vol. 21, Issue 12 https://doi.org/10.1088/0264-9381/21/12/012	journal	May 2004
Massive gravity Mukohyama, Shinji Classical and Quantum Gravity, Vol. 30, Issue 18 https://doi.org/10.1088/0264-9381/30/18/180301	journal	September 2013
Deconstructing dimensions and massive gravity de Rham, Claudia; Matas, Andrew; Tolley, Andrew J. Classical and Quantum Gravity, Vol. 31, Issue 2 https://doi.org/10.1088/0264-9381/31/2/025004	journal	November 2013
Higgs Phenomenon for 4-D Gravity in Anti de Sitter Space Porrati, Massimo Journal of High Energy Physics, Vol. 2002, Issue 04 https://doi.org/10.1088/1126-6708/2002/04/058	journal	April 2002
Ghosts in massive gravity Creminelli, Paolo; Nicolis, Alberto; Papucci, Michele Journal of High Energy Physics, Vol. 2005, Issue 09 https://doi.org/10.1088/1126-6708/2005/09/003	journal	September 2005
Nongeometric flux compactifications Shelton, Jessie; Taylor, Washington; Wecht, Brian Journal of High Energy Physics, Vol. 2005, Issue 10 https://doi.org/10.1088/1126-6708/2005/10/085	journal	October 2005
Kaluza-Klein holography Skenderis, Kostas; Taylor, Marika Journal of High Energy Physics, Vol. 2006, Issue 05 https://doi.org/10.1088/1126-6708/2006/05/057	journal	May 2006
Eigenvalues and eigenfunctions of the scalar Laplace operator on Calabi-Yau manifolds Braun, Volker; Brelidze, Tamaz; Douglas, Michael R. Journal of High Energy Physics, Vol. 2008, Issue 07 https://doi.org/10.1088/1126-6708/2008/07/120	journal	July 2008
Proof of the Payne-Pólya-Weinberger conjecture Ashbaugh, Mark S.; Benguria, Rafael D. Bulletin of the American Mathematical Society, Vol. 25, Issue 1 https://doi.org/10.1090/S0273-0979-1991-16016-7	journal	January 1991
Photons and Gravitons in S -Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass Weinberg, Steven Physical Review, Vol. 135, Issue 4B https://doi.org/10.1103/PhysRev.135.B1049	journal	August 1964
Resummation of Massive Gravity de Rham, Claudia; Gabadadze, Gregory; Tolley, Andrew J. Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.231101	journal	June 2011
(De)Constructing Dimensions Arkani-Hamed, Nima; Cohen, Andrew G.; Georgi, Howard Physical Review Letters, Vol. 86, Issue 21 https://doi.org/10.1103/PhysRevLett.86.4757	journal	May 2001
Theoretical aspects of massive gravity Hinterbichler, Kurt Reviews of Modern Physics, Vol. 84, Issue 2 https://doi.org/10.1103/RevModPhys.84.671	journal	May 2012
The conformal bootstrap: Theory, numerical techniques, and applications Poland, David; Rychkov, Slava; Vichi, Alessandro Reviews of Modern Physics, Vol. 91, Issue 1 https://doi.org/10.1103/RevModPhys.91.015002	journal	January 2019
TASI Lectures on Scattering Amplitudes Cheung, Clifford 2016 Theoretical Advanced Study Institute in Elementary Particle Physics, Anticipating the Next Discoveries in Particle Physics https://doi.org/10.1142/9789813233348_0008	conference	July 2018
Higgs Phenomenon for the Graviton in AdS Space Porrati, M. Modern Physics Letters A, Vol. 18, Issue 26 https://doi.org/10.1142/S0217732303011745	journal	August 2003
Unitarity in Gauge Symmetry Breaking on an Orbifold Abe, Y.; Haba, N.; Higashide, Y. Progress of Theoretical Physics, Vol. 109, Issue 5 https://doi.org/10.1143/PTP.109.831	journal	May 2003
Massive Gravity de Rham, Claudia Living Reviews in Relativity, Vol. 17, Issue 1 https://doi.org/10.12942/lrr-2014-7	journal	August 2014
(De)Constructing Dimensions Arkani-Hamed, Nima; Cohen, Andrew G.; Georgi, Howard The American Physical Society https://doi.org/10.17877/de290r-12313	text	January 2001
A Sharp Bound for the Ratio of the First Two Eigenvalues of Dirichlet Laplacians and Extensions Ashbaugh, Mark S.; Benguria, Rafael D. The Annals of Mathematics, Vol. 135, Issue 3 https://doi.org/10.2307/2946578	journal	May 1992
Construction de laplaciens dont une partie finie du spectre est donnée Colin de Verdière, Yves Annales scientifiques de l'École normale supérieure, Vol. 20, Issue 4 https://doi.org/10.24033/asens.1546	journal	January 1987
Resummation of Massive Gravity de Rham, Claudia; Gabadadze, Gregory; Tolley, Andrew J. arXiv https://doi.org/10.48550/arxiv.1011.1232	text	January 2010
Theoretical Aspects of Massive Gravity Hinterbichler, Kurt arXiv https://doi.org/10.48550/arxiv.1105.3735	text	January 2011
Bimetric Gravity from Ghost-free Massive Gravity Hassan, S. F.; Rosen, Rachel A. arXiv https://doi.org/10.48550/arxiv.1109.3515	text	January 2011
Interacting Spin-2 Fields Hinterbichler, Kurt; Rosen, Rachel A. arXiv https://doi.org/10.48550/arxiv.1203.5783	text	January 2012
Massive Gravity de Rham, Claudia arXiv https://doi.org/10.48550/arxiv.1401.4173	text	January 2014
Massive Spin-2 Scattering and Asymptotic Superluminality Hinterbichler, Kurt; Joyce, Austin; Rosen, Rachel A. arXiv https://doi.org/10.48550/arxiv.1708.05716	text	January 2017
Kaluza-Klein reductions and AdS/Ricci-flat correspondence Caldarelli, Marco M.; Skenderis, Kostas arXiv https://doi.org/10.48550/arxiv.1802.06085	text	January 2018
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications Poland, David; Rychkov, Slava; Vichi, Alessandro arXiv https://doi.org/10.48550/arxiv.1805.04405	text	January 2018
Non-geometric backgrounds in string theory Plauschinn, Erik arXiv https://doi.org/10.48550/arxiv.1811.11203	text	January 2018
(De)Constructing Dimensions Arkani-Hamed, Nima; Cohen, Andrew G.; Georgi, Howard arXiv https://doi.org/10.48550/arxiv.hep-th/0104005	text	January 2001
Higgs Phenomenon for 4-D Gravity in Anti de Sitter Space Porrati, M. arXiv https://doi.org/10.48550/arxiv.hep-th/0112166	text	January 2001
Higgs Phenomenon for the Graviton in Ads Space Porrati, M. arXiv https://doi.org/10.48550/arxiv.hep-th/0306253	text	January 2003
Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime Ishibashi, Akihiro; Wald, Robert M. arXiv https://doi.org/10.48550/arxiv.hep-th/0402184	text	January 2004
Ghosts in Massive Gravity Creminelli, Paolo; Nicolis, Alberto; Papucci, Michele arXiv https://doi.org/10.48550/arxiv.hep-th/0505147	text	January 2005
Nongeometric Flux Compactifications Shelton, Jessie; Taylor, Washington; Wecht, Brian arXiv https://doi.org/10.48550/arxiv.hep-th/0508133	text	January 2005
Kaluza-Klein Holography Skenderis, Kostas; Taylor, Marika arXiv https://doi.org/10.48550/arxiv.hep-th/0603016	text	January 2006
On the Stability of Riemannian Manifold with Parallel Spinors Dai, Xianzhe; Wang, Xiaodong; Wei, Guofang arXiv https://doi.org/10.48550/arxiv.math/0311253	preprint	January 2003

Cited By (2)

Amplitudes and 4D Gauss-Bonnet Theory Bonifacio, James; Hinterbichler, Kurt; Johnson, Laura A. arXiv https://doi.org/10.48550/arxiv.2004.10716	text	January 2020
Scattering amplitudes of massive spin-2 Kaluza-Klein states grow only as O ( s ) Chivukula, R. Sekhar; Foren, Dennis; Mohan, Kirtimaan A. Physical Review D, Vol. 101, Issue 5 https://doi.org/10.1103/physrevd.101.055013	journal	March 2020

Similar Records

Bootstrap bounds on closed Einstein manifolds

Journal Article · Sun Oct 11 20:00:00 EDT 2020 · Journal of High Energy Physics (Online) · OSTI ID:1852887

Black branes in flux compactifications

Journal Article · Tue Oct 01 00:00:00 EDT 2013 · Journal of High Energy Physics (Online) · OSTI ID:1090327

Conformal invariance on Calabi-Yau spaces

Conference · Tue Jul 01 00:00:00 EDT 1986 · OSTI ID:5107808

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics

Unitarization from geometry

Citation Formats

References (71)

Cited By (2)

Similar Records

Related Subjects