Abstract
We explore possible extensions of the Weak Gravity Conjecture (WGC) to scalar field theories. To avoid charged black hole remnants, the WGC requires the existence of a particle with a mass m ≤ gqMP, with charge q and U(1) gauge coupling g, allowing the decay to shed the black hole charge. Although there is no obvious problem that arises in the absence of a U(1) charge, it has been postulated that gravity must remain the weakest force even when extended to scalar interactions. Quantifying this conjecture may be done by comparing scalar and gravitational amplitudes, or as we advocate here by comparing scattering cross sections. In theories with non-trivial field space geometries, by working out examples with perturbation theory around arbitrary field values and performing tadpole resummations, we argue that the conjecture must be applied only at extrema of the scalar potential (when expressed in locally canonical coordinates). We consider several toy models in the context of no-scale supergravity and also consider examples of inflationary models.
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].
H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [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].
E. Palti, The Weak Gravity Conjecture and Scalar Fields, JHEP 08 (2017) 034 [arXiv:1705.04328] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Repulsive Forces and the Weak Gravity Conjecture, JHEP 10 (2019) 055 [arXiv:1906.02206] [INSPIRE].
D. Lust and E. Palti, Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture, JHEP 02 (2018) 040 [arXiv:1709.01790] [INSPIRE].
E. Gonzalo and L.E. Ibáñez, A Strong Scalar Weak Gravity Conjecture and Some Implications, JHEP 08 (2019) 118 [arXiv:1903.08878] [INSPIRE].
B. Freivogel, T. Gasenzer, A. Hebecker and S. Leonhardt, A conjecture on the Minimal Size of Bound States, SciPost Phys. 8 (2020) 058 [arXiv:1912.09485] [INSPIRE].
M. Scalisi and I. Valenzuela, Swampland distance conjecture, inflation and α-attractors, JHEP 08 (2019) 160 [arXiv:1812.07558] [INSPIRE].
S. Shirai and M. Yamazaki, Is Gravity the Weakest Force?, Class. Quant. Grav. 38 (2021) 035006 [arXiv:1904.10577] [INSPIRE].
A. Kusenko, V. Takhistov, M. Yamada and M. Yamazaki, Fundamental Forces and Scalar Field Dynamics in the Early Universe, Phys. Lett. B 804 (2020) 135369 [arXiv:1908.10930] [INSPIRE].
D. Andriot, N. Cribiori and D. Erkinger, The web of swampland conjectures and the TCC bound, JHEP 07 (2020) 162 [arXiv:2004.00030] [INSPIRE].
E. Gonzalo and L.E. Ibáñez, Pair Production and Gravity as the Weakest Force, JHEP 12 (2020) 039 [arXiv:2005.07720] [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].
M. Etheredge et al., Sharpening the Distance Conjecture in diverse dimensions, JHEP 12 (2022) 114 [arXiv:2206.04063] [INSPIRE].
K. Benakli, C. Branchina and G. Lafforgue-Marmet, Revisiting the scalar weak gravity conjecture, Eur. Phys. J. C 80 (2020) 742 [arXiv:2004.12476] [INSPIRE].
E. Dudas, T. Gherghetta, K.A. Olive and S. Verner, Supergravity scattering amplitudes, Phys. Rev. D 108 (2023) 076024 [arXiv:2302.05456] [INSPIRE].
R. Alonso, E.E. Jenkins and A.V. Manohar, A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space, Phys. Lett. B 754 (2016) 335 [arXiv:1511.00724] [INSPIRE].
R. Alonso, E.E. Jenkins and A.V. Manohar, Geometry of the Scalar Sector, JHEP 08 (2016) 101 [arXiv:1605.03602] [INSPIRE].
T. Cohen, N. Craig, X. Lu and D. Sutherland, Unitarity violation and the geometry of Higgs EFTs, JHEP 12 (2021) 003 [arXiv:2108.03240] [INSPIRE].
R. Alonso and M. West, Roads to the Standard Model, Phys. Rev. D 105 (2022) 096028 [arXiv:2109.13290] [INSPIRE].
C. Cheung, A. Helset and J. Parra-Martinez, Geometric soft theorems, JHEP 04 (2022) 011 [arXiv:2111.03045] [INSPIRE].
C. Cheung, A. Helset and J. Parra-Martinez, Geometry-kinematics duality, Phys. Rev. D 106 (2022) 045016 [arXiv:2202.06972] [INSPIRE].
A. Helset, E.E. Jenkins and A.V. Manohar, Geometry in scattering amplitudes, Phys. Rev. D 106 (2022) 116018 [arXiv:2210.08000] [INSPIRE].
E. Cremmer, S. Ferrara, C. Kounnas and D.V. Nanopoulos, Naturally Vanishing Cosmological Constant in N = 1 Supergravity, Phys. Lett. B 133 (1983) 61 [INSPIRE].
A.B. Lahanas and D.V. Nanopoulos, The Road to No Scale Supergravity, Phys. Rept. 145 (1987) 1 [INSPIRE].
E. Witten, Dimensional Reduction of Superstring Models, Phys. Lett. B 155 (1985) 151 [INSPIRE].
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
J. Ellis et al., Building models of inflation in no-scale supergravity, Int. J. Mod. Phys. D 29 (2020) 2030011 [arXiv:2009.01709] [INSPIRE].
J. Ellis, D.V. Nanopoulos and K.A. Olive, No-Scale Supergravity Realization of the Starobinsky Model of Inflation, Phys. Rev. Lett. 111 (2013) 111301 [Erratum ibid. 111 (2013) 129902] [arXiv:1305.1247] [INSPIRE].
R. Kallosh and A. Linde, Superconformal generalizations of the Starobinsky model, JCAP 06 (2013) 028 [arXiv:1306.3214] [INSPIRE].
M.A.G. Garcia, K. Kaneta, Y. Mambrini and K.A. Olive, Reheating and Post-inflationary Production of Dark Matter, Phys. Rev. D 101 (2020) 123507 [arXiv:2004.08404] [INSPIRE].
E. Dudas, G. Pradisi, M. Nicolosi and A. Sagnotti, On tadpoles and vacuum redefinitions in string theory, Nucl. Phys. B 708 (2005) 3 [hep-th/0410101] [INSPIRE].
H.P. Nilles, Supersymmetry, Supergravity and Particle Physics, Phys. Rept. 110 (1984) 1 [INSPIRE].
K. Higashijima and M. Nitta, Kahler normal coordinate expansion in supersymmetric theories, Prog. Theor. Phys. 105 (2001) 243 [hep-th/0006027] [INSPIRE].
K. Higashijima, E. Itou and M. Nitta, Normal coordinates in Kahler manifolds and the background field method, Prog. Theor. Phys. 108 (2002) 185 [hep-th/0203081] [INSPIRE].
A. Hatzinikitas, A Note on Riemann normal coordinates, hep-th/0001078 [INSPIRE].
B.R. Holstein, Graviton Physics, Am. J. Phys. 74 (2006) 1002 [gr-qc/0607045] [INSPIRE].
S. Clery, Y. Mambrini, K.A. Olive and S. Verner, Gravitational portals in the early Universe, Phys. Rev. D 105 (2022) 075005 [arXiv:2112.15214] [INSPIRE].
J.R. Ellis, A.B. Lahanas, D.V. Nanopoulos and K. Tamvakis, No-Scale Supersymmetric Standard Model, Phys. Lett. B 134 (1984) 429 [INSPIRE].
J.R. Ellis, C. Kounnas and D.V. Nanopoulos, Phenomenological SU(1,1) Supergravity, Nucl. Phys. B 241 (1984) 406 [INSPIRE].
J.R. Ellis, C. Kounnas and D.V. Nanopoulos, No Scale Supersymmetric Guts, Nucl. Phys. B 247 (1984) 373 [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
A. Linde, Y. Mambrini and K.A. Olive, Supersymmetry Breaking due to Moduli Stabilization in String Theory, Phys. Rev. D 85 (2012) 066005 [arXiv:1111.1465] [INSPIRE].
J. Ellis, D.V. Nanopoulos and K.A. Olive, Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity, JCAP 10 (2013) 009 [arXiv:1307.3537] [INSPIRE].
J. Ellis, D.V. Nanopoulos, K.A. Olive and S. Verner, A general classification of Starobinsky-like inflationary avatars of SU(2,1)/SU(2) × U(1) no-scale supergravity, JHEP 03 (2019) 099 [arXiv:1812.02192] [INSPIRE].
S. Ferrara, A. Kehagias and A. Riotto, The Imaginary Starobinsky Model, Fortsch. Phys. 62 (2014) 573 [arXiv:1403.5531] [INSPIRE].
S. Ferrara, A. Kehagias and A. Riotto, The Imaginary Starobinsky Model and Higher Curvature Corrections, Fortsch. Phys. 63 (2015) 2 [arXiv:1405.2353] [INSPIRE].
R. Kallosh, A. Linde, B. Vercnocke and W. Chemissany, Is Imaginary Starobinsky Model Real?, JCAP 07 (2014) 053 [arXiv:1403.7189] [INSPIRE].
K. Hamaguchi, T. Moroi and T. Terada, Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result, Phys. Lett. B 733 (2014) 305 [arXiv:1403.7521] [INSPIRE].
J. Ellis, M.A.G. García, D.V. Nanopoulos and K.A. Olive, Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2, JCAP 05 (2014) 037 [arXiv:1403.7518] [INSPIRE].
J. Ellis, M.A.G. Garcia, D.V. Nanopoulos and K.A. Olive, A No-Scale Inflationary Model to Fit Them All, JCAP 08 (2014) 044 [arXiv:1405.0271] [INSPIRE].
J. Ellis, M.A.G. García, D.V. Nanopoulos and K.A. Olive, Two-Field Analysis of No-Scale Supergravity Inflation, JCAP 01 (2015) 010 [arXiv:1409.8197] [INSPIRE].
T. Li, Z. Li and D.V. Nanopoulos, No-Scale Ripple Inflation Revisited, JCAP 04 (2014) 018 [arXiv:1310.3331] [INSPIRE].
C.P. Burgess, M. Cicoli and F. Quevedo, String Inflation After Planck 2013, JCAP 11 (2013) 003 [arXiv:1306.3512] [INSPIRE].
F. Farakos, A. Kehagias and A. Riotto, On the Starobinsky Model of Inflation from Supergravity, Nucl. Phys. B 876 (2013) 187 [arXiv:1307.1137] [INSPIRE].
S. Ferrara, R. Kallosh, A. Linde and M. Porrati, Minimal Supergravity Models of Inflation, Phys. Rev. D 88 (2013) 085038 [arXiv:1307.7696] [INSPIRE].
W. Buchmüller, V. Domcke and C. Wieck, No-scale D-term inflation with stabilized moduli, Phys. Lett. B 730 (2014) 155 [arXiv:1309.3122] [INSPIRE].
C. Pallis, Linking Starobinsky-Type Inflation in no-Scale Supergravity to MSSM, JCAP 04 (2014) 024 [Erratum ibid. 07 (2017) E01] [arXiv:1312.3623] [INSPIRE].
C. Pallis, Induced-Gravity Inflation in no-Scale Supergravity and Beyond, JCAP 08 (2014) 057 [arXiv:1403.5486] [INSPIRE].
I. Antoniadis, E. Dudas, S. Ferrara and A. Sagnotti, The Volkov–Akulov–Starobinsky supergravity, Phys. Lett. B 733 (2014) 32 [arXiv:1403.3269] [INSPIRE].
T. Li, Z. Li and D.V. Nanopoulos, Chaotic Inflation in No-Scale Supergravity with String Inspired Moduli Stabilization, Eur. Phys. J. C 75 (2015) 55 [arXiv:1405.0197] [INSPIRE].
W. Buchmuller, E. Dudas, L. Heurtier and C. Wieck, Large-Field Inflation and Supersymmetry Breaking, JHEP 09 (2014) 053 [arXiv:1407.0253] [INSPIRE].
T. Terada, Y. Watanabe, Y. Yamada and J. Yokoyama, Reheating processes after Starobinsky inflation in old-minimal supergravity, JHEP 02 (2015) 105 [arXiv:1411.6746] [INSPIRE].
W. Buchmuller et al., Challenges for Large-Field Inflation and Moduli Stabilization, JHEP 04 (2015) 058 [arXiv:1501.05812] [INSPIRE].
A.B. Lahanas and K. Tamvakis, Inflation in no-scale supergravity, Phys. Rev. D 91 (2015) 085001 [arXiv:1501.06547] [INSPIRE].
M.C. Romao and S.F. King, Starobinsky-like inflation in no-scale supergravity Wess-Zumino model with Polonyi term, JHEP 07 (2017) 033 [arXiv:1703.08333] [INSPIRE].
M. Galante, R. Kallosh, A. Linde and D. Roest, Unity of Cosmological Inflation Attractors, Phys. Rev. Lett. 114 (2015) 141302 [arXiv:1412.3797] [INSPIRE].
B.J. Broy, M. Galante, D. Roest and A. Westphal, Pole inflation — Shift symmetry and universal corrections, JHEP 12 (2015) 149 [arXiv:1507.02277] [INSPIRE].
S. Cecotti, Higher derivative supergravity is equivalent to standard supergravity coupled to matter. 1, Phys. Lett. B 190 (1987) 86 [INSPIRE].
J.R. Ellis, C. Kounnas and D.V. Nanopoulos, No Scale Supergravity Models with a Planck Mass Gravitino, Phys. Lett. B 143 (1984) 410 [INSPIRE].
J. Ellis, M.A.G. Garcia, D.V. Nanopoulos and K.A. Olive, Phenomenological Aspects of No-Scale Inflation Models, JCAP 10 (2015) 003 [arXiv:1503.08867] [INSPIRE].
J. Ellis, D.V. Nanopoulos, K.A. Olive and S. Verner, Phenomenology and Cosmology of No-Scale Attractor Models of Inflation, JCAP 08 (2020) 037 [arXiv:2004.00643] [INSPIRE].
I.M. Rasulian, M. Torabian and L. Velasco-Sevilla, Swampland de Sitter conjectures in no-scale supergravity models, Phys. Rev. D 104 (2021) 044028 [arXiv:2105.14501] [INSPIRE].
Acknowledgments
We would like to thank E. Gonzalo, L. Ibanez, M. Luty, and E. Palti for useful discussions. The work of T.G and K.A.O. was supported in part by DOE grant DE-SC0011842 at the University of Minnesota. The work of T.G. was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. The work of S.V. was supported in part by DOE grant DE-SC0022148.
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: 2305.11636
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
Dudas, E., Gherghetta, T., Olive, K.A. et al. Testing the scalar weak gravity conjecture in no-scale supergravity. J. High Energ. Phys. 2024, 249 (2024). https://doi.org/10.1007/JHEP05(2024)249
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2024)249