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Quantum Gravity Constraints from Unitarity and Analyticity

Bellazzini, Brando and Cheung, Clifford and Remmen, Grant N. (2016) Quantum Gravity Constraints from Unitarity and Analyticity. Physical Review D, 93 (6). Art. No. 064076. ISSN 2470-0010. doi:10.1103/PhysRevD.93.064076.

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We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In D≥4 spacetime dimensions, these consistency conditions mandate positive coefficients for certain quartic curvature operators. We systematically enumerate all such positivity bounds in D=4 and D=5 before extending to D≥6. Afterwards, we derive positivity bounds for supersymmetric operators and verify that all of our constraints are satisfied by weakly coupled string theories. Among quadratic curvature operators, we find that the Gauss-Bonnet term in D≥5 is inconsistent unless new degrees of freedom enter at the natural cutoff scale defined by the effective theory. Our bounds apply to perturbative ultraviolet completions of gravity.

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Remmen, Grant N.0000-0001-6569-8866
Additional Information:© 2016 American Physical Society. Received 5 January 2016; published 29 March 2016. We thank Nima Arkani-Hamed and John Schwarz for useful discussions and comments. B. B. is supported in part by the MIUR-FIRB Grant No. RBFR12H1MW, by the Agence Nationale de la Recherche under Contract No. ANR 2010 BLANC 0413 01, and by the ERC Starting Grant agreement No. 278234 “NewDark” project. C. C. is supported by a Sloan Research Fellowship and a DOE Early Career Award under Grant No. DE-SC0010255. G. N. R. is supported by a Hertz Graduate Fellowship and a NSF Graduate Research Fellowship under Grant No. DGE-1144469. B. B. and C. C. thank the Aspen Center for Physics and the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence “Origin and Structure of the Universe” for their hospitality and support while this work was in progress.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR)RBFR12H1MW
Agence Nationale pour la Recherche (ANR)ANR 2010 BLANC 0413 01
European Research Council (ERC)278234
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0010255
Fannie and John Hertz FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1144469
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Issue or Number:6
Record Number:CaltechAUTHORS:20151022-115252221
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:61420
Deposited By: Joy Painter
Deposited On:22 Oct 2015 20:27
Last Modified:10 Nov 2021 22:48

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