Advertisement

Journal of High Energy Physics

, 2017:43 | Cite as

Weak gravity conjecture, multiple point principle and the standard model landscape

  • Yuta Hamada
  • Gary Shiu
Open Access
Regular Article - Theoretical Physics

Abstract

The requirement for an ultraviolet completable theory to be well-behaved upon compactification has been suggested as a guiding principle for distinguishing the landscape from the swampland. Motivated by the weak gravity conjecture and the multiple point principle, we investigate the vacuum structure of the standard model compactified on S1 and T 2. The measured value of the Higgs mass implies, in addition to the electroweak vacuum, the existence of a new vacuum where the Higgs field value is around the Planck scale. We explore two- and three-dimensional critical points of the moduli potential arising from compactifications of the electroweak vacuum as well as this high scale vacuum, in the presence of Majorana/Dirac neutrinos and/or axions. We point out potential sources of instability for these lower dimensional critical points in the standard model landscape. We also point out that a high scale AdS4 vacuum of the Standard Model, if exists, would be at odd with the conjecture that all non-supersymmetric AdS vacua are unstable. We argue that, if we require a degeneracy between three- and four-dimensional vacua as suggested by the multiple point principle, the neutrinos are predicted to be Dirac, with the mass of the lightest neutrino \( \approx \mathcal{O}\left(1-10\right) \) meV, which may be tested by future CMB, large scale structure and 21cm line observations.

Keywords

Field Theories in Lower Dimensions Neutrino Physics Flux compactifications 

Notes

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.

References

  1. [1]
    C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].
  2. [2]
    N. Arkani-Hamed, S. Dubovsky, A. Nicolis and G. Villadoro, Quantum Horizons of the Standard Model Landscape, JHEP 06 (2007) 078 [hep-th/0703067] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    J.M. Arnold, B. Fornal and M.B. Wise, Standard Model Vacua for Two-dimensional Compactifications, JHEP 12 (2010) 083 [arXiv:1010.4302] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J.M. Arnold, B. Fornal and K. Ishiwata, Finite Temperature Structure of the Compactified Standard Model, JHEP 08 (2011) 030 [arXiv:1103.0002] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  5. [5]
    B. Fornal and M.B. Wise, Standard model with compactified spatial dimensions, JHEP 07 (2011) 086 [arXiv:1106.0890] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
  7. [7]
    CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
  8. [8]
    G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    Y. Hamada, H. Kawai and K.-y. Oda, Bare Higgs mass at Planck scale, Phys. Rev. D 87 (2013) 053009 [Erratum ibid. D 89 (2014) 059901] [arXiv:1210.2538] [INSPIRE].
  10. [10]
    D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    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].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    C. Cheung and G.N. Remmen, Naturalness and the Weak Gravity Conjecture, Phys. Rev. Lett. 113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    A. de la Fuente, P. Saraswat and R. Sundrum, Natural Inflation and Quantum Gravity, Phys. Rev. Lett. 114 (2015) 151303 [arXiv:1412.3457] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation, JHEP 10 (2015) 023 [arXiv:1503.04783] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    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].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    T.C. Bachlechner, C. Long and L. McAllister, Planckian Axions and the Weak Gravity Conjecture, JHEP 01 (2016) 091 [arXiv:1503.07853] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    J. Brown, W. Cottrell, G. Shiu and P. Soler, On Axionic Field Ranges, Loopholes and the Weak Gravity Conjecture, JHEP 04 (2016) 017 [arXiv:1504.00659] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  18. [18]
    D. Junghans, Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture, JHEP 02 (2016) 128 [arXiv:1504.03566] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    B. Heidenreich, M. Reece and T. Rudelius, Weak Gravity Strongly Constrains Large-Field Axion Inflation, JHEP 12 (2015) 108 [arXiv:1506.03447] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  20. [20]
    K. Kooner, S. Parameswaran and I. Zavala, Warping the Weak Gravity Conjecture, Phys. Lett. B 759 (2016) 402 [arXiv:1509.07049] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  21. [21]
    D. Harlow, Wormholes, Emergent Gauge Fields and the Weak Gravity Conjecture, JHEP 01 (2016) 122 [arXiv:1510.07911] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    L.E. Ibáñez, M. Montero, A. Uranga and I. Valenzuela, Relaxion Monodromy and the Weak Gravity Conjecture, JHEP 04 (2016) 020 [arXiv:1512.00025] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  23. [23]
    M. Montero, G. Shiu and P. Soler, The Weak Gravity Conjecture in three dimensions, JHEP 10 (2016) 159 [arXiv:1606.08438] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    W. Cottrell, G. Shiu and P. Soler, Weak Gravity Conjecture and Extremal Black Holes, PoS(CORFU2016)130 [arXiv:1611.06270] [INSPIRE].
  25. [25]
    A. Hebecker, P. Henkenjohann and L.T. Witkowski, What is the Magnetic Weak Gravity Conjecture for Axions?, Fortsch. Phys. 65 (2017) 1700011 [arXiv:1701.06553] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    E. Palti, The Weak Gravity Conjecture and Scalar Fields, JHEP 08 (2017) 034 [arXiv:1705.04328] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    B. Heidenreich, M. Reece and T. Rudelius, Sharpening the Weak Gravity Conjecture with Dimensional Reduction, JHEP 02 (2016) 140 [arXiv:1509.06374] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    B. Heidenreich, M. Reece and T. Rudelius, Evidence for a sublattice weak gravity conjecture, JHEP 08 (2017) 025 [arXiv:1606.08437] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    M. Montero, A.M. Uranga and I. Valenzuela, A Chern-Simons Pandemic, JHEP 07 (2017) 123 [arXiv:1702.06147] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, arXiv:1610.01533 [INSPIRE].
  31. [31]
    B. Freivogel and M. Kleban, Vacua Morghulis, arXiv:1610.04564 [INSPIRE].
  32. [32]
    U. Danielsson and G. Dibitetto, Fate of stringy AdS vacua and the weak gravity conjecture, Phys. Rev. D 96 (2017) 026020 [arXiv:1611.01395] [INSPIRE].ADSGoogle Scholar
  33. [33]
    C.D. Froggatt and H.B. Nielsen, Standard model criticality prediction: Top mass 173 ± 5 GeV and Higgs mass 135 ± 9 GeV, Phys. Lett. B 368 (1996) 96 [hep-ph/9511371] [INSPIRE].
  34. [34]
    D.L. Bennett, Multiple point criticality, nonlocality, and fine tuning in fundamental physics: Predictions for gauge coupling constants gives α −1 = 136.8 ± 9, Ph.D. Thesis, Bohr Institute (1996) [hep-ph/9607341].
  35. [35]
    Y. Hamada, H. Kawai and K.-y. Oda, Eternal Higgs inflation and the cosmological constant problem, Phys. Rev. D 92 (2015) 045009 [arXiv:1501.04455] [INSPIRE].ADSMathSciNetGoogle Scholar
  36. [36]
    Y. Hamada, H. Kawai and K. Kawana, Evidence of the Big Fix, Int. J. Mod. Phys. A 29 (2014) 1450099 [arXiv:1405.1310] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    Y. Hamada, H. Kawai and K. Kawana, Weak Scale From the Maximum Entropy Principle, PTEP 2015 (2015) 033B06 [arXiv:1409.6508] [INSPIRE].
  38. [38]
    Y. Hamada, H. Kawai and K. Kawana, Natural solution to the naturalness problem: The universe does fine-tuning, PTEP 2015 (2015) 123B03 [arXiv:1509.05955] [INSPIRE].
  39. [39]
    H.B. Nielsen, PREdicted the Higgs Mass, Bled Workshops Phys. 13 (2012) 94 [arXiv:1212.5716] [INSPIRE].Google Scholar
  40. [40]
    S.M. Carroll, M.C. Johnson and L. Randall, Dynamical compactification from de Sitter space, JHEP 11 (2009) 094 [arXiv:0904.3115] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    L.E. Ibáñez, V. Martin-Lozano and I. Valenzuela, Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture, arXiv:1706.05392 [INSPIRE].
  42. [42]
    Y. Hamada, H. Kawai, K.-y. Oda and S.C. Park, Higgs inflation from Standard Model criticality, Phys. Rev. D 91 (2015) 053008 [arXiv:1408.4864] [INSPIRE].ADSGoogle Scholar
  43. [43]
    KamLAND collaboration, A. Gando et al., Reactor On-Off Antineutrino Measurement with KamLAND, Phys. Rev. D 88 (2013) 033001 [arXiv:1303.4667] [INSPIRE].
  44. [44]
    T. Banks, TASI Lectures on Holographic Space-Time, SUSY and Gravitational Effective Field Theory, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2010). String Theory and Its Applications: From meV to the Planck Scale, Boulder, Colorado, U.S.A., 1-25 June 2010 [arXiv:1007.4001].
  45. [45]
    E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B 195 (1982) 481 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  46. [46]
    J.J. Blanco-Pillado, B. Shlaer, K. Sousa and J. Urrestilla, Bubbles of Nothing and Supersymmetric Compactifications, JCAP 10 (2016) 002 [arXiv:1606.03095] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  49. [49]
    P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
  51. [51]
    S.M. Bilenky and C. Giunti, Neutrinoless double-beta decay: A brief review, Mod. Phys. Lett. A 27 (2012) 1230015 [arXiv:1203.5250] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  52. [52]
    G. Mellema et al., Reionization and the Cosmic Dawn with the Square Kilometre Array, Exper. Astron. 36 (2013) 235 [arXiv:1210.0197] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    POLARBEAR collaboration, A. Suzuki et al., The POLARBEAR-2 and the Simons Array Experiment, J. Low. Temp. Phys. 184 (2016) 805 [arXiv:1512.07299] [INSPIRE].
  54. [54]
    DESI collaboration, M. Levi et al., The DESI Experiment, a whitepaper for Snowmass 2013, arXiv:1308.0847 [INSPIRE].
  55. [55]
    A. Liu, J.R. Pritchard, R. Allison, A.R. Parsons, U. Seljak and B.D. Sherwin, Eliminating the optical depth nuisance from the CMB with 21 cm cosmology, Phys. Rev. D 93 (2016) 043013 [arXiv:1509.08463] [INSPIRE].ADSGoogle Scholar
  56. [56]
    Y. Oyama, K. Kohri and M. Hazumi, Constraints on the neutrino parameters by future cosmological 21 cm line and precise CMB polarization observations, JCAP 02 (2016) 008 [arXiv:1510.03806] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    M.S. Turner and L. Widrow, The Bianchi Models and New Inflation, (1986) [INSPIRE].
  58. [58]
    E. Elizalde, Multidimensional extension of the generalized Chowla-Selberg formula, Commun. Math. Phys. 198 (1998) 83 [hep-th/9707257] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  59. [59]
    E. Ponton and E. Poppitz, Casimir energy and radius stabilization in five-dimensional orbifolds and six-dimensional orbifolds, JHEP 06 (2001) 019 [hep-ph/0105021] [INSPIRE].
  60. [60]
    M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Avalon Publishing (1995).Google Scholar
  61. [61]
    S. Moroz, Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence, Phys. Rev. D 81 (2010) 066002 [arXiv:0911.4060] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of Wisconsin-MadisonMadisonU.S.A.
  2. 2.KEK Theory Center, IPNS, KEKTsukubaJapan

Personalised recommendations