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A new mechanism for symmetry breaking from nilmanifolds

A preprint version of the article is available at arXiv.

Abstract

We present a method to obtain a scalar potential at tree level from a pure gauge theory on nilmanifolds, a class of negatively-curved compact spaces, and discuss the spontaneous symmetry breaking mechanism induced in the residual Minkowski space after compactification at low energy. We show that the scalar potential is completely determined by the gauge symmetries and the geometry of the compact manifold. In order to allow for simple analytic calculations we consider three extra space dimensions as the minimal example of a nilmanifold, therefore considering a pure Yang-Mills theory in seven dimensions.

References

  1. I. Antoniadis, A possible new dimension at a few TeV, Phys. Lett. B 246 (1990) 377 [INSPIRE].

    ADS  Article  Google Scholar 

  2. 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].

  3. I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, New dimensions at a millimeter to a Fermi and superstrings at a TeV, Phys. Lett. B 436 (1998) 257 [hep-ph/9804398] [INSPIRE].

  4. G.F. Giudice, R. Rattazzi and J.D. Wells, Quantum gravity and extra dimensions at high-energy colliders, Nucl. Phys. B 544 (1999) 3 [hep-ph/9811291] [INSPIRE].

  5. N. Arkani-Hamed and M. Schmaltz, Hierarchies without symmetries from extra dimensions, Phys. Rev. D 61 (2000) 033005 [hep-ph/9903417] [INSPIRE].

  6. G. Cacciapaglia, A. Deandrea and N. Deutschmann, Dark matter and localised fermions from spherical orbifolds?, JHEP 04 (2016) 083 [arXiv:1601.00081] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  7. N. Manton, A new six-dimensional approach to the Weinberg-Salam model, Nucl. Phys. B 158 (1979) 141.

    ADS  Article  Google Scholar 

  8. Y. Hosotani, Dynamical mass generation by compact extra dimensions, Phys. Lett. B 126 (1983) 309.

    ADS  Article  Google Scholar 

  9. N. Haba, Y. Hosotani, Y. Kawamura and T. Yamashita, Dynamical symmetry breaking in gauge Higgs unification on orbifold, Phys. Rev. D 70 (2004) 015010 [hep-ph/0401183] [INSPIRE].

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

  11. Y. Hosotani and M. Mabe, Higgs boson mass and electroweak-gravity hierarchy from dynamical gauge-Higgs unification in the warped spacetime, Phys. Lett. B 615 (2005) 257 [hep-ph/0503020] [INSPIRE].

  12. A.D. Medina, N.R. Shah and C.E.M. Wagner, Gauge-Higgs unification and radiative electroweak symmetry breaking in warped extra dimensions, Phys. Rev. D 76 (2007) 095010 [arXiv:0706.1281] [INSPIRE].

  13. Y. Hosotani, K. Oda, T. Ohnuma and Y. Sakamura, Dynamical electroweak symmetry breaking in SO(5) × U(1) gauge-Higgs unification with top and bottom quarks, Phys. Rev. D 78 (2008) 096002 [Erratum ibid. D 79 (2009) 079902] [arXiv:0806.0480] [INSPIRE].

  14. Y. Hosotani and N. Yamatsu, Gauge–Higgs grand unification, PTEP 2015 (2015) 111B01 [arXiv:1504.03817] [INSPIRE].

  15. I. Antoniadis, K. Benakli and M. Quirós, Radiative symmetry breaking in brane models, Nucl. Phys. B 583 (2000) 35 [hep-ph/0004091] [INSPIRE].

  16. S. Chang, J. Hisano, H. Nakano, N. Okada and M. Yamaguchi, Bulk standard model in the Randall-Sundrum background, Phys. Rev. D 62 (2000) 084025 [hep-ph/9912498] [INSPIRE].

  17. N. Kaloper, J. March-Russell, G.D. Starkman and M. Trodden, Compact hyperbolic extra dimensions: Branes, Kaluza-Klein modes and cosmology, Phys. Rev. Lett. 85 (2000) 928 [hep-ph/0002001] [INSPIRE].

  18. D. Orlando and S.C. Park, Compact hyperbolic extra dimensions: a M-theory solution and its implications for the LHC, JHEP 08 (2010) 006 [arXiv:1006.1901] [INSPIRE].

    ADS  Article  Google Scholar 

  19. S. Nasri, P.J. Silva, G.D. Starkman and M. Trodden, Radion stabilization in compact hyperbolic extra dimensions, Phys. Rev. D 66 (2002) 045029 [hep-th/0201063] [INSPIRE].

  20. S. Kachru, M.B. Schulz, P.K. Tripathy and S.P. Trivedi, New supersymmetric string compactifications, JHEP 03 (2003) 061 [hep-th/0211182] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  21. M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A scan for new N = 1 vacua on twisted tori, JHEP 05 (2007) 031 [hep-th/0609124] [INSPIRE].

  22. C. Caviezel et al., The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets, Class. Quant. Grav. 26 (2009) 025014 [arXiv:0806.3458] [INSPIRE].

  23. D. Andriot, New supersymmetric vacua on solvmanifolds, JHEP 02 (2016) 112 [arXiv:1507.00014] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  24. D. Andriot, M. Larfors, D. Lüst and P. Patalong, (Non-)commutative closed string on T-dual toroidal backgrounds, JHEP 06 (2013) 021 [arXiv:1211.6437] [INSPIRE].

  25. D. Andriot et al., Towards Kaluza-Klein dark matter on nilmanifolds, JHEP 06 (2016) 169 [arXiv:1603.02289] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  26. D. Andriot and D. Tsimpis, Laplacian spectrum on a nilmanifold, truncations and effective theories, JHEP 09 (2018) 096 [arXiv:1806.05156] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  27. M. Gell-Mann, Symmetries of baryons and mesons, Phys. Rev. 125 (1962) 1067 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  28. I. Antoniadis, K. Benakli and M. Quirós, Finite Higgs mass without supersymmetry, New J. Phys. 3 (2001) 20 [hep-th/0108005] [INSPIRE].

  29. D. Andriot, E. Goi, R. Minasian and M. Petrini, Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory, JHEP 05 (2011) 028 [arXiv:1003.3774] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

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Correspondence to Aldo Deandrea.

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ArXiv ePrint: 2002.11128

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Andriot, D., Cornell, A., Deandrea, A. et al. A new mechanism for symmetry breaking from nilmanifolds. J. High Energ. Phys. 2020, 122 (2020). https://doi.org/10.1007/JHEP05(2020)122

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  • DOI: https://doi.org/10.1007/JHEP05(2020)122

Keywords

  • Beyond Standard Model
  • Field Theories in Higher Dimensions
  • Large Extra Dimensions