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Heterotic M-theory from the clockwork perspective

A preprint version of the article is available at arXiv.


Compactifications of heterotic M-theory are shown to provide solutions to the weak- and axion-scale hierarchy problems as a consequence of warped large extra dimensions. They allow a description that is reminiscent of the so-called continuous clockwork mechanism. The models constructed here cover a new region of clockwork parameter space and exhibit unexplored spectra and couplings of Kaluza-Klein modes. Previously discussed models are outside this region of parameter space and do seem to require an ultraviolet completion other than that of perturbative higher dimensional D = 10, 11 string- or M-theory. A 5D-supergravity description can be given for all explicitly known continuous clockwork models. The various classes of models can be distinguished through the different roles played by vector multiplets and the universal hypermultiplet in 5D-supergravity.


  1. N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, The Hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [INSPIRE].

  2. L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].

  3. I. Antoniadis, S. Dimopoulos and A. Giveon, Little string theory at a TeV, JHEP 05 (2001) 055 [hep-th/0103033] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  4. K. Choi, S.H. Im and C.S. Shin, General Continuum Clockwork, JHEP 07 (2018) 113 [arXiv:1711.06228] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].

  6. J.E. Kim, H.P. Nilles and M. Peloso, Completing natural inflation, JCAP 01 (2005) 005 [hep-ph/0409138] [INSPIRE].

  7. R. Kappl, S. Krippendorf and H.P. Nilles, Aligned Natural Inflation: Monodromies of two Axions, Phys. Lett. B 737 (2014) 124 [arXiv:1404.7127] [INSPIRE].

  8. K. Choi, H. Kim and S. Yun, Natural inflation with multiple sub-Planckian axions, Phys. Rev. D 90 (2014) 023545 [arXiv:1404.6209] [INSPIRE].

  9. T. Higaki, K.S. Jeong, N. Kitajima and F. Takahashi, The QCD Axion from Aligned Axions and Diphoton Excess, Phys. Lett. B 755 (2016) 13 [arXiv:1512.05295] [INSPIRE].

  10. P.W. Graham, D.E. Kaplan and S. Rajendran, Cosmological Relaxation of the Electroweak Scale, Phys. Rev. Lett. 115 (2015) 221801 [arXiv:1504.07551] [INSPIRE].

    ADS  Article  Google Scholar 

  11. K. Choi and S.H. Im, Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry, JHEP 01 (2016) 149 [arXiv:1511.00132] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  12. D.E. Kaplan and R. Rattazzi, Large field excursions and approximate discrete symmetries from a clockwork axion, Phys. Rev. D 93 (2016) 085007 [arXiv:1511.01827] [INSPIRE].

  13. N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett. 86 (2001)4757 [hep-th/0104005] [INSPIRE].

  14. C.T. Hill, S. Pokorski and J. Wang, Gauge Invariant Effective Lagrangian for Kaluza-Klein Modes, Phys. Rev. D 64 (2001) 105005 [hep-th/0104035] [INSPIRE].

  15. G.F. Giudice and M. McCullough, A Clockwork Theory, JHEP 02 (2017) 036 [arXiv:1610.07962] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  16. N. Craig, I. Garcia Garcia and D. Sutherland, Disassembling the Clockwork Mechanism, JHEP 10 (2017) 018 [arXiv:1704.07831] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  17. G.F. Giudice and M. McCullough, Comment on “Disassembling the Clockwork Mechanism”, arXiv:1705.10162 [INSPIRE].

  18. P. Saraswat, Weak gravity conjecture and effective field theory, Phys. Rev. D 95 (2017) 025013 [arXiv:1608.06951] [INSPIRE].

  19. N. Fonseca, L. de Lima, C.S. Machado and R.D. Matheus, Large field excursions from a few site relaxion model, Phys. Rev. D 94 (2016) 015010 [arXiv:1601.07183] [INSPIRE].

  20. A. Kehagias and A. Riotto, Clockwork Inflation, Phys. Lett. B 767 (2017) 73 [arXiv:1611.03316] [INSPIRE].

  21. S.H. Im, H.P. Nilles and A. Trautner, Exploring extra dimensions through inflationary tensor modes, JHEP 03 (2018) 004 [arXiv:1707.03830] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  22. M. Farina, D. Pappadopulo, F. Rompineve and A. Tesi, The photo-philic QCD axion, JHEP 01 (2017) 095 [arXiv:1611.09855] [INSPIRE].

    ADS  Article  Google Scholar 

  23. A. Ahmed and B.M. Dillon, Clockwork Goldstone Bosons, Phys. Rev. D 96 (2017) 115031 [arXiv:1612.04011] [INSPIRE].

  24. T. Hambye, D. Teresi and M.H.G. Tytgat, A Clockwork WIMP, JHEP 07 (2017) 047 [arXiv:1612.06411] [INSPIRE].

    ADS  Article  Google Scholar 

  25. G. von Gersdorff, Natural Fermion Hierarchies from Random Yukawa Couplings, JHEP 09 (2017)094 [arXiv:1705.05430] [INSPIRE].

  26. R. Coy, M. Frigerio and M. Ibe, Dynamical Clockwork Axions, JHEP 10 (2017) 002 [arXiv:1706.04529] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  27. I. Ben-Dayan, Generalized Clockwork Theory, arXiv:1706.05308 [INSPIRE].

  28. D.K. Hong, D.H. Kim and C.S. Shin, Clockwork graviton contributions to muon g − 2, Phys. Rev. D 97 (2018) 035014 [arXiv:1706.09376] [INSPIRE].

  29. S.C. Park and C.S. Shin, Clockwork seesaw mechanisms, Phys. Lett. B 776 (2018) 222 [arXiv:1707.07364] [INSPIRE].

  30. H.M. Lee, Gauged U(1) clockwork theory, Phys. Lett. B 778 (2018) 79 [arXiv:1708.03564] [INSPIRE].

  31. P. Agrawal, G. Marques-Tavares and W. Xue, Opening up the QCD axion window, JHEP 03 (2018) 049 [arXiv:1708.05008] [INSPIRE].

  32. J. Kim and J. McDonald, Clockwork Higgs portal model for freeze-in dark matter, Phys. Rev. D 98 (2018) 023533 [arXiv:1709.04105] [INSPIRE].

  33. P. Agrawal, J. Fan, M. Reece and L.-T. Wang, Experimental Targets for Photon Couplings of the QCD Axion, JHEP 02 (2018) 006 [arXiv:1709.06085] [INSPIRE].

    ADS  Article  Google Scholar 

  34. K.S. Jeong and C.S. Shin, Peccei-Quinn Relaxion, JHEP 01 (2018) 121 [arXiv:1709.10025] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  35. O. Davidi, R.S. Gupta, G. Perez, D. Redigolo and A. Shalit, The Nelson-Barr Relaxion, arXiv:1711.00858 [INSPIRE].

  36. A. Ibarra, A. Kushwaha and S.K. Vempati, Clockwork for Neutrino Masses and Lepton Flavor Violation, Phys. Lett. B 780 (2018) 86 [arXiv:1711.02070] [INSPIRE].

  37. K.M. Patel, Clockwork mechanism for flavor hierarchies, Phys. Rev. D 96 (2017) 115013 [arXiv:1711.05393] [INSPIRE].

  38. M. Dine, L. Stephenson Haskins, L. Ubaldi and D. Xu, Some Remarks on Anthropic Approaches to the Strong CP Problem, JHEP 05 (2018) 171 [arXiv:1801.03466] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  39. J.M. Cline and J.R. Espinosa, Axionic landscape for Higgs coupling near-criticality, Phys. Rev. D 97 (2018) 035025 [arXiv:1801.03926] [INSPIRE].

  40. K. Choi, H. Kim and T. Sekiguchi, Late-Time Magnetogenesis Driven by Axionlike Particle Dark Matter and a Dark Photon, Phys. Rev. Lett. 121 (2018) 031102 [arXiv:1802.07269] [INSPIRE].

  41. A.J. Long, Cosmological Aspects of the Clockwork Axion, JHEP 07 (2018) 066 [arXiv:1803.07086] [INSPIRE].

    ADS  Article  Google Scholar 

  42. G. Marques-Tavares and M. Teo, Light axions with large hadronic couplings, JHEP 05 (2018) 180 [arXiv:1803.07575] [INSPIRE].

  43. Q. Bonnefoy, E. Dudas and S. Pokorski, Axions in a highly protected gauge symmetry model, arXiv:1804.01112 [INSPIRE].

  44. J. Kim and J. Mcdonald, Freeze-In Dark Matter from a sub-Higgs Mass Clockwork Sector via the Higgs Portal, Phys. Rev. D 98 (2018) 123503 [arXiv:1804.02661] [INSPIRE].

  45. F. Niedermann, A. Padilla and P.M. Saffin, Higher Order Clockwork Gravity, Phys. Rev. D 98 (2018)104014 [arXiv:1805.03523] [INSPIRE].

  46. O. Davidi, R.S. Gupta, G. Perez, D. Redigolo and A. Shalit, The hierarchion, a relaxion addressing the Standard Model’s hierarchies, JHEP 08 (2018) 153 [arXiv:1806.08791] [INSPIRE].

    ADS  Article  Google Scholar 

  47. K. Choi, S. Lee, H. Seong and S. Yun, Gamma-ray spectral modulations induced by photon-ALP-dark photon oscillations, arXiv:1806.09508 [INSPIRE].

  48. P. Agrawal, J. Fan and M. Reece, Clockwork Axions in Cosmology: Is Chromonatural Inflation Chrononatural?, JHEP 10 (2018) 193 [arXiv:1806.09621] [INSPIRE].

    ADS  Article  Google Scholar 

  49. A. Goudelis, K.A. Mohan and D. Sengupta, Clockworking FIMPs, JHEP 10 (2018) 014 [arXiv:1807.06642] [INSPIRE].

  50. R. Alonso, A. Carmona, B.M. Dillon, J.F. Kamenik, J. Martin Camalich and J. Zupan, A clockwork solution to the flavor puzzle, JHEP 10 (2018) 099 [arXiv:1807.09792] [INSPIRE].

    ADS  Article  Google Scholar 

  51. S.C. Park and C.S. Shin, Clockwork Higgs inflation, arXiv:1807.09952 [INSPIRE].

  52. A. Banerjee, S. Ghosh and T.S. Ray, Clockworked VEVs and Neutrino Mass, JHEP 11 (2018) 075 [arXiv:1808.04010] [INSPIRE].

  53. N. Craig and I. Garcia Garcia, Rescuing Massive Photons from the Swampland, JHEP 11 (2018) 067 [arXiv:1810.05647] [INSPIRE].

  54. R.T. Co, A. Pierce, Z. Zhang and Y. Zhao, Dark Photon Dark Matter Produced by Axion Oscillations, arXiv:1810.07196 [INSPIRE].

  55. P. Agrawal, N. Kitajima, M. Reece, T. Sekiguchi and F. Takahashi, Relic Abundance of Dark Photon Dark Matter, arXiv:1810.07188 [INSPIRE].

  56. A. Kehagias and A. Riotto, The Clockwork Supergravity, JHEP 02 (2018) 160 [arXiv:1710.04175] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  57. I. Antoniadis, A. Delgado, C. Markou and S. Pokorski, The effective supergravity of Little String Theory, Eur. Phys. J. C 78 (2018) 146 [arXiv:1710.05568] [INSPIRE].

  58. G.F. Giudice, Y. Kats, M. McCullough, R. Torre and A. Urbano, Clockwork/linear dilaton: structure and phenomenology, JHEP 06 (2018) 009 [arXiv:1711.08437] [INSPIRE].

    ADS  Article  Google Scholar 

  59. I. Antoniadis, A. Arvanitaki, S. Dimopoulos and A. Giveon, Phenomenology of TeV Little String Theory from Holography, Phys. Rev. Lett. 108 (2012) 081602 [arXiv:1102.4043] [INSPIRE].

  60. S. Stieberger, (0, 2) heterotic gauge couplings and their M-theory origin, Nucl. Phys. B 541 (1999) 109 [hep-th/9807124] [INSPIRE].

  61. E. Witten, Strong coupling expansion of Calabi-Yau compactification, Nucl. Phys. B 471 (1996) 135 [hep-th/9602070] [INSPIRE].

  62. H.P. Nilles, M. Olechowski and M. Yamaguchi, Supersymmetry breaking and soft terms in M-theory, Phys. Lett. B 415 (1997) 24 [hep-th/9707143] [INSPIRE].

  63. H.P. Nilles, M. Olechowski and M. Yamaguchi, Supersymmetry breakdown at a hidden wall, Nucl. Phys. B 530 (1998) 43 [hep-th/9801030] [INSPIRE].

  64. A. Lukas, B.A. Ovrut and D. Waldram, On the four-dimensional effective action of strongly coupled heterotic string theory, Nucl. Phys. B 532 (1998) 43 [hep-th/9710208] [INSPIRE].

  65. A. Lukas, B.A. Ovrut, K.S. Stelle and D. Waldram, The Universe as a domain wall, Phys. Rev. D 59 (1999) 086001 [hep-th/9803235] [INSPIRE].

  66. A. Kehagias, Exponential and power law hierarchies from supergravity, Phys. Lett. B 469 (1999) 123 [hep-th/9906204] [INSPIRE].

  67. D. Teresi, Clockwork without supersymmetry, Phys. Lett. B 783 (2018) 1 [arXiv:1802.01591] [INSPIRE].

  68. A. Lukas, B.A. Ovrut, K.S. Stelle and D. Waldram, Heterotic M-theory in five-dimensions, Nucl. Phys. B 552 (1999) 246 [hep-th/9806051] [INSPIRE].

  69. K. Behrndt and S. Gukov, Domain walls and superpotentials from M-theory on Calabi-Yau three folds, Nucl. Phys. B 580 (2000) 225 [hep-th/0001082] [INSPIRE].

  70. S.H. Im, H.P. Nilles and M. Olechowski, Axion Clockworks from heterotic M-theory, in preparation.

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Correspondence to Sang Hui Im.

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Im, S.H., Nilles, H.P. & Olechowski, M. Heterotic M-theory from the clockwork perspective. J. High Energ. Phys. 2019, 151 (2019).

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  • M-Theory
  • Supergravity Models
  • Superstrings and Heterotic Strings
  • Large Extra Dimensions