Abstract
We develop a framework to derive consistency constraints on gravitational Regge amplitudes based on the finite energy sum rules (FESRs), which directly connect gravitational Regge amplitudes at a finite ultraviolet scale with infrared physics without suffering from super-Planckian physics. For illustration, we consider four-point scattering of an identical massless scalar coupled to gravity. First, we derive multiple FESRs without relying on the s-t-u permutation invariance. We then make use of FESRs, crossing symmetry, and other principles such as unitarity, to derive bounds on the Regge parameters. The bounds result in infrared finite gravitational positivity bounds in four spacetime dimensions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].
T.D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland, and the Missing Corner, PoS TASI2017 (2017) 015 [arXiv:1711.00864] [INSPIRE].
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
M. van Beest, J. Calderón-Infante, D. Mirfendereski and I. Valenzuela, Lectures on the Swampland Program in String Compactifications, Phys. Rept. 989 (2022) 1 [arXiv:2102.01111] [INSPIRE].
T.N. Pham and T.N. Truong, Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation, Phys. Rev. D 31 (1985) 3027 [INSPIRE].
A. Adams et al., Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The String landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
Y. Hamada, T. Noumi and G. Shiu, Weak Gravity Conjecture from Unitarity and Causality, Phys. Rev. Lett. 123 (2019) 051601 [arXiv:1810.03637] [INSPIRE].
B. Bellazzini, M. Lewandowski and J. Serra, Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity, Phys. Rev. Lett. 123 (2019) 251103 [arXiv:1902.03250] [INSPIRE].
N. Arkani-Hamed, Y.-T. Huang, J.-Y. Liu and G.N. Remmen, Causality, unitarity, and the weak gravity conjecture, JHEP 03 (2022) 083 [arXiv:2109.13937] [INSPIRE].
T. Noumi and H. Satake, Higher derivative corrections to black brane thermodynamics and the weak gravity conjecture, JHEP 12 (2022) 130 [arXiv:2210.02894] [INSPIRE].
C. Cheung and G.N. Remmen, Infrared Consistency and the Weak Gravity Conjecture, JHEP 12 (2014) 087 [arXiv:1407.7865] [INSPIRE].
S. Andriolo, D. Junghans, T. Noumi and G. Shiu, A Tower Weak Gravity Conjecture from Infrared Consistency, Fortsch. Phys. 66 (2018) 1800020 [arXiv:1802.04287] [INSPIRE].
W.-M. Chen, Y.-T. Huang, T. Noumi and C. Wen, Unitarity bounds on charged/neutral state mass ratios, Phys. Rev. D 100 (2019) 025016 [arXiv:1901.11480] [INSPIRE].
L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley, QED positivity bounds, Phys. Rev. D 103 (2021) 125020 [arXiv:2012.05798] [INSPIRE].
K. Aoki, T.Q. Loc, T. Noumi and J. Tokuda, Is the Standard Model in the Swampland? Consistency Requirements from Gravitational Scattering, Phys. Rev. Lett. 127 (2021) 091602 [arXiv:2104.09682] [INSPIRE].
T. Noumi and J. Tokuda, Gravitational positivity bounds on scalar potentials, Phys. Rev. D 104 (2021) 066022 [arXiv:2105.01436] [INSPIRE].
T. Noumi, S. Sato and J. Tokuda, Phenomenological Motivation for Gravitational Positivity Bounds: A Case Study of Dark Sector Physics, arXiv:2205.12835 [INSPIRE].
K. Häring and A. Zhiboedov, Gravitational Regge bounds, arXiv:2202.08280 [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, Sharp boundaries for the swampland, JHEP 07 (2021) 110 [arXiv:2102.08951] [INSPIRE].
S. Caron-Huot, Y.-Z. Li, J. Parra-Martinez and D. Simmons-Duffin, Causality constraints on corrections to Einstein gravity, JHEP 05 (2023) 122 [arXiv:2201.06602] [INSPIRE].
J. Tokuda, K. Aoki and S. Hirano, Gravitational positivity bounds, JHEP 11 (2020) 054 [arXiv:2007.15009] [INSPIRE].
M. Herrero-Valea, R. Santos-Garcia and A. Tokareva, Massless positivity in graviton exchange, Phys. Rev. D 104 (2021) 085022 [arXiv:2011.11652] [INSPIRE].
L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley, Reverse Bootstrapping: IR Lessons for UV Physics, Phys. Rev. Lett. 128 (2022) 051602 [arXiv:2111.09226] [INSPIRE].
M. Herrero-Valea, A.S. Koshelev and A. Tokareva, UV graviton scattering and positivity bounds from IR dispersion relations, Phys. Rev. D 106 (2022) 105002 [arXiv:2205.13332] [INSPIRE].
L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley, Positivity Bounds and the Massless Spin-2 Pole, Phys. Rev. D 102 (2020) 125023 [arXiv:2007.12667] [INSPIRE].
B. Bellazzini, M. Riembau and F. Riva, IR side of positivity bounds, Phys. Rev. D 106 (2022) 105008 [arXiv:2112.12561] [INSPIRE].
K. Igi, pi-N Scattering Length and Singularities in the Complex J Plane, Phys. Rev. Lett. 9 (1962) 76 [INSPIRE].
A.A. Logunov, L.D. Soloviev and A.N. Tavkhelidze, Dispersion sum rules and high-energy scattering, Phys. Lett. B 24 (1967) 181 [INSPIRE].
K. Igi and S. Matsuda, New Sum Rules and Singularities in the Complex J Plane, Phys. Rev. Lett. 18 (1967) 625 [INSPIRE].
R. Gatto, New Sum Rules for Superconvergence, Phys. Rev. Lett. 18 (1967) 803 [INSPIRE].
R. Dolen, D. Horn and C. Schmid, Prediction of Regge Parameters of rho Poles from Low-Energy pi N Data, Phys. Rev. Lett. 19 (1967) 402 [INSPIRE].
R. Dolen, D. Horn and C. Schmid, Finite energy sum rules and their application to pi N charge exchange, Phys. Rev. 166 (1968) 1768 [INSPIRE].
M. Ademollo, H.R. Rubinstein, G. Veneziano and M.A. Virasoro, Bootstraplike Conditions from Superconvergence, Phys. Rev. Lett. 19 (1967) 1402 [INSPIRE].
M. Ademollo, H.R. Rubinstein, G. Veneziano and M.A. Virasoro, Bootstrap of meson trajectories from superconvergence, Phys. Rev. 176 (1968) 1904 [INSPIRE].
G. Veneziano, Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cim. A 57 (1968) 190 [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, JHEP 05 (2021) 259 [arXiv:2012.15849] [INSPIRE].
B. Bellazzini et al., Positive moments for scattering amplitudes, Phys. Rev. D 104 (2021) 036006 [arXiv:2011.00037] [INSPIRE].
S. Caron-Huot and V. Van Duong, Extremal Effective Field Theories, JHEP 05 (2021) 280 [arXiv:2011.02957] [INSPIRE].
A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou, New positivity bounds from full crossing symmetry, JHEP 05 (2021) 255 [arXiv:2011.02400] [INSPIRE].
A. Sinha and A. Zahed, Crossing Symmetric Dispersion Relations in Quantum Field Theories, Phys. Rev. Lett. 126 (2021) 181601 [arXiv:2012.04877] [INSPIRE].
C. de Rham, S. Jaitly and A.J. Tolley, Constraints on Regge behaviour from IR physics, arXiv:2212.04975 [INSPIRE].
Acknowledgments
We thank Yu-tin Huang for useful discussion. T.N. was supported in part by JSPS KAKENHI Grant No. 20H01902 and No. 22H01220, and MEXT KAKENHI Grant No. 21H00075, No. 21H05184 and No. 21H05462. J.T. was supported by IBS under the project code, IBSR018- D1, and JSPS KAKENHI Grant No. 20J00912 and No. 21K13922.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2212.08001
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Noumi, T., Tokuda, J. Finite energy sum rules for gravitational Regge amplitudes. J. High Energ. Phys. 2023, 32 (2023). https://doi.org/10.1007/JHEP06(2023)032
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2023)032