Abstract
We propose a new version of the scalar Weak Gravity Conjecture (WGC) which would apply to any scalar field coupled to quantum gravity. For a single scalar it is given by the differential constraint (V″)2 ≤ (2V‴2 − V″V′′′′)\( {M}_{\mathrm{p}}^2 \), where V is the scalar potential. It corresponds to the statement that self-interactions of a scalar must be stronger than gravity for any value of the scalar field. We find that the solutions which saturate the bound correspond to towers of extremal states with mass \( {m}^2\left(\phi \right)={m}_0^2/\left({\left(R/m\right)}^2+1/{(nR)}^2\right) \), with R2 = eϕ, consistent with the emergence of an extra dimension at large or small R and the existence of extended objects (strings). These states act as WGC states for the scalar ϕ. It is also consistent with the distance swampland conjecture with a built-in duality symmetry. All of this is remarkable since neither extra dimensions nor string theory are put in the theory from the beginning, but they emerge. This is quite analogous to how the 11-th dimension appears in M-theory from towers of Type IIA solitonic D0-branes. From this constraint one can derive several swampland conjectures from a single principle. In particular one finds that an axion potential is only consistent if f ≤ Mp, recovering a result already conjectured from other arguments. The conjecture has far reaching consequences and applies to several interesting physical systems: i) Among chaotic inflation potentials only those asymptotically linear may survive. ii) If applied to the radion of the circle compactification of the Standard Model to 3D with Dirac neutrinos, the constraint implies that the 4D cosmological constant scale must be larger than the mass of the lightest neutrino, which must be in normal hierarchy. It also puts a constraint on the EW scale, potentially explaining the hierarchy problem. This recovers and improves results already obtained by applying the AdS swampland conjecture, but in a way which is independent from UV physics. iii) It also constraints simplest moduli fixing string models. The simplest KKLT model is compatible with the constraints but the latter may be relevant for some choices of parameters.
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].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP06 (2007) 060 [hep-th/0601001] [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].
T. Rudelius, Constraints on Axion Inflation from the Weak Gravity Conjecture, JCAP09 (2015) 020 [arXiv:1503.00795] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, Transplanckian axions!?, JHEP08 (2015) 032 [arXiv:1503.03886] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation, JHEP10 (2015) 023 [arXiv:1503.04783] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, On Axionic Field Ranges, Loopholes and the Weak Gravity Conjecture, JHEP04 (2016) 017 [arXiv:1504.00659] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Weak Gravity Strongly Constrains Large-Field Axion Inflation, JHEP12 (2015) 108 [arXiv:1506.03447] [INSPIRE].
A. de la Fuente, P. Saraswat and R. Sundrum, Natural Inflation and Quantum Gravity, Phys. Rev. Lett.114 (2015) 151303 [arXiv:1412.3457] [INSPIRE].
A. Hebecker, P. Mangat, F. Rompineve and L.T. Witkowski, Winding out of the Swamp: Evading the Weak Gravity Conjecture with F-term Winding Inflation?, Phys. Lett.B 748 (2015) 455 [arXiv:1503.07912] [INSPIRE].
T.C. Bachlechner, C. Long and L. McAllister, Planckian Axions and the Weak Gravity Conjecture, JHEP01 (2016) 091 [arXiv:1503.07853] [INSPIRE].
T. Rudelius, On the Possibility of Large Axion Moduli Spaces, JCAP04 (2015) 049 [arXiv:1409.5793] [INSPIRE].
D. Junghans, Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture, JHEP02 (2016) 128 [arXiv:1504.03566] [INSPIRE].
K. Kooner, S. Parameswaran and I. Zavala, Warping the Weak Gravity Conjecture, Phys. Lett.B 759 (2016) 402 [arXiv:1509.07049] [INSPIRE].
D. Harlow, Wormholes, Emergent Gauge Fields and the Weak Gravity Conjecture, JHEP01 (2016) 122 [arXiv:1510.07911] [INSPIRE].
L.E. Ibáñez, M. Montero, A. Uranga and I. Valenzuela, Relaxion Monodromy and the Weak Gravity Conjecture, JHEP04 (2016) 020 [arXiv:1512.00025] [INSPIRE].
A. Hebecker, F. Rompineve and A. Westphal, Axion Monodromy and the Weak Gravity Conjecture, JHEP04 (2016) 157 [arXiv:1512.03768] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Evidence for a sublattice weak gravity conjecture, JHEP08 (2017) 025 [arXiv:1606.08437] [INSPIRE].
M. Montero, G. Shiu and P. Soler, The Weak Gravity Conjecture in three dimensions, JHEP10 (2016) 159 [arXiv:1606.08438] [INSPIRE].
P. Saraswat, Weak gravity conjecture and effective field theory, Phys. Rev.D 95 (2017) 025013 [arXiv:1608.06951] [INSPIRE].
D. Klaewer and E. Palti, Super-Planckian Spatial Field Variations and Quantum Gravity, JHEP01 (2017) 088 [arXiv:1610.00010] [INSPIRE].
L. McAllister, P. Schwaller, G. Servant, J. Stout and A. Westphal, Runaway Relaxion Monodromy, JHEP02 (2018) 124 [arXiv:1610.05320] [INSPIRE].
A. Herráez and L.E. Ibáñez, An Axion-induced SM/MSSM Higgs Landscape and the Weak Gravity Conjecture, JHEP02 (2017) 109 [arXiv:1610.08836] [INSPIRE].
M. Montero, Are tiny gauge couplings out of the Swampland?, JHEP10 (2017) 208 [arXiv:1708.02249] [INSPIRE].
L.E. Ibáñez and M. Montero, A Note on the WGC, Effective Field Theory and Clockwork within String Theory, JHEP02 (2018) 057 [arXiv:1709.02392] [INSPIRE].
G. Aldazabal and L.E. Ibáñez, A Note on 4D Heterotic String Vacua, FI-terms and the Swampland, Phys. Lett.B 782 (2018) 375 [arXiv:1804.07322] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Proof of the Weak Gravity Conjecture from Black Hole Entropy, JHEP10 (2018) 004 [arXiv:1801.08546] [INSPIRE].
T.W. Grimm, E. Palti and I. Valenzuela, Infinite Distances in Field Space and Massless Towers of States, JHEP08 (2018) 143 [arXiv:1802.08264] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Emergence of Weak Coupling at Large Distance in Quantum Gravity, Phys. Rev. Lett.121 (2018) 051601 [arXiv:1802.08698] [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].
R. Blumenhagen, D. Kläwer, L. Schlechter and F. Wolf, The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces, JHEP06 (2018) 052 [arXiv:1803.04989] [INSPIRE].
A. Landete and G. Shiu, Mass Hierarchies and Dynamical Field Range, Phys. Rev.D 98 (2018) 066012 [arXiv:1806.01874] [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].
S.-J. Lee, W. Lerche and T. Weigand, Tensionless Strings and the Weak Gravity Conjecture, JHEP10 (2018) 164 [arXiv:1808.05958] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Modular Fluxes, Elliptic Genera and Weak Gravity Conjectures in Four Dimensions, arXiv:1901.08065 [INSPIRE].
T.D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland and the Missing Corner, PoS(TASI2017) 015 (2017) [arXiv:1711.00864] [INSPIRE].
E. Palti, The Weak Gravity Conjecture and Scalar Fields, JHEP08 (2017) 034 [arXiv:1705.04328] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, A Stringy Test of the Scalar Weak Gravity Conjecture, Nucl. Phys. B938 (2019) 321 [arXiv:1810.05169] [INSPIRE].
D. Lüst and E. Palti, Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture, JHEP02 (2018) 040 [arXiv:1709.01790] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
P. Agrawal, G. Obied, P.J. Steinhardt and C. Vafa, On the Cosmological Implications of the String Swampland, Phys. Lett.B 784 (2018) 271 [arXiv:1806.09718] [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, arXiv:1807.05193 [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett.B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].
G. Dvali and C. Gomez, On Exclusion of Positive Cosmological Constant, Fortsch. Phys.67 (2019) 1800092 [arXiv:1806.10877] [INSPIRE].
G. Dvali, C. Gomez and S. Zell, Quantum Breaking Bound on de Sitter and Swampland, Fortsch. Phys.67 (2019) 1800094 [arXiv:1810.11002] [INSPIRE].
D. Andriot, On the de Sitter swampland criterion, Phys. Lett. B785 (2018) 570 [arXiv:1806.10999] [INSPIRE].
C. Roupec and T. Wrase, de Sitter Extrema and the Swampland, Fortsch. Phys.67 (2019) 1800082 [arXiv:1807.09538] [INSPIRE].
J.P. Conlon, The de Sitter swampland conjecture and supersymmetric AdS vacua, Int. J. Mod. Phys.A 33 (2018) 1850178 [arXiv:1808.05040] [INSPIRE].
S. Kachru and S.P. Trivedi, A comment on effective field theories of flux vacua, Fortsch. Phys.67 (2019) 1800086 [arXiv:1808.08971] [INSPIRE].
H. Murayama, M. Yamazaki and T.T. Yanagida, Do We Live in the Swampland?, JHEP12 (2018) 032 [arXiv:1809.00478] [INSPIRE].
G. Buratti, E. García-Valdecasas and A.M. Uranga, Supersymmetry Breaking Warped Throats and the Weak Gravity Conjecture, JHEP04 (2019) 111 [arXiv:1810.07673] [INSPIRE].
M. Montero, A Holographic Derivation of the Weak Gravity Conjecture, JHEP03 (2019) 157 [arXiv:1812.03978] [INSPIRE].
C. Córdova, G.B. De Luca and A. Tomasiello, Classical de Sitter Solutions of 10-Dimensional Supergravity, Phys. Rev. Lett.122 (2019) 091601 [arXiv:1812.04147] [INSPIRE].
G. Buratti, J. Calderón and A.M. Uranga, Transplanckian axion monodromy!?, JHEP05 (2019) 176 [arXiv:1812.05016] [INSPIRE].
T.W. Grimm, C. Li and E. Palti, Infinite Distance Networks in Field Space and Charge Orbits, JHEP03 (2019) 016 [arXiv:1811.02571] [INSPIRE].
A.D. Linde, Chaotic Inflation, Phys. Lett.129B (1983) 177 [INSPIRE].
E. Silverstein and A. Westphal, Monodromy in the CMB: Gravity Waves and String Inflation, Phys. Rev.D 78 (2008) 106003 [arXiv:0803.3085] [INSPIRE].
L. McAllister, E. Silverstein and A. Westphal, Gravity Waves and Linear Inflation from Axion Monodromy, Phys. Rev.D 82 (2010) 046003 [arXiv:0808.0706] [INSPIRE].
L. McAllister, E. Silverstein, A. Westphal and T. Wrase, The Powers of Monodromy, JHEP09 (2014) 123 [arXiv:1405.3652] [INSPIRE].
X. Dong, B. Horn, E. Silverstein and A. Westphal, Simple exercises to flatten your potential, Phys. Rev.D 84 (2011) 026011 [arXiv:1011.4521] [INSPIRE].
F. Marchesano, D. Regalado and G. Zoccarato, U(1) mixing and D-brane linear equivalence, JHEP08 (2014) 157 [arXiv:1406.2729] [INSPIRE].
D. Baumann and L. McAllister, Inflation and String Theory, arXiv:1404.2601 [INSPIRE].
L.E. Ibáñez and I. Valenzuela, The Higgs Mass as a Signature of Heavy SUSY, JHEP05 (2013) 064 [arXiv:1301.5167] [INSPIRE].
L.E. Ibáñez, F. Marchesano and I. Valenzuela, Higgs-otic Inflation and String Theory, JHEP01 (2015) 128 [arXiv:1411.5380] [INSPIRE].
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett.B 91 (1980) 99 [INSPIRE].
V.F. Mukhanov and G.V. Chibisov, Quantum Fluctuations and a Nonsingular Universe, JETP Lett.33 (1981) 532 [Pisma Zh. Eksp. Teor. Fiz.33 (1981) 549] [INSPIRE].
F. Bezrukov, The Higgs field as an inflaton, Class. Quant. Grav.30 (2013) 214001 [arXiv:1307.0708] [INSPIRE].
N. Arkani-Hamed, S. Dubovsky, A. Nicolis and G. Villadoro, Quantum Horizons of the Standard Model Landscape, JHEP06 (2007) 078 [hep-th/0703067] [INSPIRE].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, Adv. Theor. Math. Phys.21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].
L.E. Ibáñez, V. Martin-Lozano and I. Valenzuela, Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture, JHEP11 (2017) 066 [arXiv:1706.05392] [INSPIRE].
E. Gonzalo, A. Herráez and L.E. Ibáñez, AdS-phobia, the WGC, the Standard Model and Supersymmetry, JHEP06 (2018) 051 [arXiv:1803.08455] [INSPIRE].
E. Gonzalo and L.E. Ibáñez, The Fundamental Need for a SM Higgs and the Weak Gravity Conjecture, Phys. Lett.B 786 (2018) 272 [arXiv:1806.09647] [INSPIRE].
Y. Hamada and G. Shiu, Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape, JHEP11 (2017) 043 [arXiv:1707.06326] [INSPIRE].
J.R. Espinosa, E. Gonzalo and L.E. Ibáñez, in progress (2019).
G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
C. Cheung and G.N. Remmen, Naturalness and the Weak Gravity Conjecture, Phys. Rev. Lett.113 (2014) 051601 [arXiv:1402.2287] [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].
R. Blumenhagen, D. Kläwer and L. Schlechter, Swampland Variations on a Theme by KKLT, JHEP05 (2019) 152 [arXiv:1902.07724] [INSPIRE].
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
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1903.08878
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Gonzalo, E., Ibáñez, L.E. A Strong Scalar Weak Gravity Conjecture and some implications. J. High Energ. Phys. 2019, 118 (2019). https://doi.org/10.1007/JHEP08(2019)118
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2019)118