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Dimensional reduction via a novel Higgs mechanism

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Abstract

Many theories of quantum gravity live in higher dimensions, and their reduction to four dimensions via mechanisms such as Kaluza–Klein compactification or brane world models have associated problems. We propose a novel mechanism of dimensional reduction via spontaneous symmetry breaking of a higher dimensional local Lorentz group to one in lower dimensions. Working in the gauge theory formulation of gravity, we couple a Higgs field to spin connections, include a potential for the field, and show that for a suitable choice of Higgs vacuum, the local Lorentz symmetry of the action gets spontaneously reduced to one in a lower dimension. Thus effectively the dimension of spacetime gets reduced by one. This provides a viable mechanism for the dimensional reduction, and may have applications in theories of quantum gravity.

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References

  1. Green, M.B., Schwarz, J.H., Witten, E.: Superstring Theory, vol. I and II. Cambridge University Press, Cambridge (1987)

    MATH  Google Scholar 

  2. Scherk, J., Schwarz, J.H.: Phys. Lett. B 57, 463 (1975)

    Article  ADS  Google Scholar 

  3. Rubakov, V.A., Shaposhnikov, M.E.: Phys. Lett. B 125, 136 (1983)

    Article  ADS  Google Scholar 

  4. Arkani-Hamed, N., Dimopoulos, S., Dvali, G.: Phys. Lett. B 429, 263–272 (1998)

    Article  ADS  Google Scholar 

  5. Randall, L., Sundrum, R.: Phys. Rev. Lett. 83, 3370–3373 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  6. Chatrchyan, S., et al.: (CMS Collaboration), JHEP 1209, 094 (2012)

  7. Neupane, I.P.: Phys. Rev. D 90(12), 123502 (2014)

    Article  ADS  Google Scholar 

  8. Buchbinder, I.L., Odintsov, S.D.: Class. Quant. Grav. 2, 721–731 (1985)

    Article  ADS  Google Scholar 

  9. Elizalde, E., Odintsov, S.D., Romeo, A.: Phys. Rev. D 51, 4250 (1995). [arXiv:hep-th/9410028]

    Article  ADS  Google Scholar 

  10. Zee, A.: Phys. Rev. Lett. 42, 417 (1979)

    Article  ADS  Google Scholar 

  11. Magueijo, J., Smolin, L.: Class. Quant. Grav. 21, 1725 (2004). [gr-qc/0305055]

    Article  ADS  Google Scholar 

  12. Percacci, R.: Phys. Lett. 144B, 37 (1984)

    Article  ADS  Google Scholar 

  13. Percacci, R.: Nucl. Phys. B 353, 271 (1991). [arXiv:0712.3545 [hep-th]]

    Article  ADS  Google Scholar 

  14. Kostelecky, V.A., Samuel, S.: Phys. Rev. D 39, 683 (1989)

    Article  ADS  Google Scholar 

  15. Shapiro, I.L., Takata, H.: Phys. Rev. D 52, 2162 (1995). arXiv:hep-th/9502111

    Article  ADS  Google Scholar 

  16. Bluhm, R., Kostelecky, A.: Phys. Rev. D 71, 065008 (2005). arXiv:hep-th/0412230

    Article  ADS  Google Scholar 

  17. Kirsch, I.: Phys. Rev. D 72, 024001 (2005). arXiv:hep-th/0503024

    Article  ADS  MathSciNet  Google Scholar 

  18. Leclerc, M.: Ann. Phys. 321, 708 (2006). [gr-qc/0502005]

    Article  ADS  Google Scholar 

  19. Wever, C.S.P.: A Higgs mechanism for gravity. University of Utrecht Master’s Thesis (2009)

  20. Chamseddine, A.H., Mukhanov, V.: JHEP 1208, 036 (2012). [arXiv:1205.5828 [hep-th]]

    Article  ADS  Google Scholar 

  21. Moffat, J.W.: Class. Quant. Grav. 27, 135016 (2010). [arXiv:0905.1668 [hep-th]]

    Article  ADS  Google Scholar 

  22. Moffat, J.W.: Found. Phys. 23, 411 (1993). [gr-qc/9209001]

    Article  ADS  MathSciNet  Google Scholar 

  23. Das, S., Ghosh, S.: arXiv:1006.5774, 1108.2163

  24. Krasnov, K.: Phys. Rev. D 85, 125023 (2012). [arXiv:1112.5097 [hep-th]]

    Article  ADS  Google Scholar 

  25. Arraut, I.: Europhys. Lett. 111, 61001 (2015). [arXiv:1509.08338]

    Article  ADS  Google Scholar 

  26. Das, S., Faizal, M., Vagenas, E.C.: arXiv:1805.08665 (IJMPD, to appear)

  27. Ramond, P.: Field theory: a modern primer. Front. Phys. 74, 1 (1989)

    Google Scholar 

  28. Feynman, R.P.: Feynman Lectures on Gravitation. Addison-Wesley, Boston (1995)

    Google Scholar 

  29. Deser, S.: Class. Quant. Grav. 4, L99 (1987)

    Article  ADS  Google Scholar 

  30. Lovelock, D.: Arch. Rat. Mech. Anal. 33, 54 (1969)

    Article  Google Scholar 

  31. Cottingham, W.N., Greenwood, D.A.: An Introduction to the Standard Model of Particle Physics, 2nd edn. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  32. Cheng, T., Li, L.: Gauge Theory of Elementary Particle Physics. Oxford University Press, Oxford (1982)

    Google Scholar 

  33. Lovelock, D.: J. Math. Phys. 12, 498 (1971)

    Article  ADS  Google Scholar 

  34. Zwiebach, B.: Phys. Lett. B 156, 315 (1985)

    Article  ADS  Google Scholar 

  35. Boulware, D.G., Deser, S.: Phys. Rev. Lett. 55, 2656 (1985)

    Article  ADS  Google Scholar 

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Acknowledgements

We thank P. Diaz, G. Kunstatter, R. B. Mann, J. Moffat, D. Smith, E. C. Vagenas and M. Walton for discussions. We thank the Referees for their useful comments. This work is supported by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Theoretical Physics Group and Quantum Alberta, Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, AB, T1K 3M4, Canada

    Saurya Das & Mir Faizal

  2. Irving K. Barber School of Arts and Sciences, University of British Columbia - Okanagan, Kelowna, BC, V1V 1V7, Canada

    Mir Faizal

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  1. Saurya Das
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  2. Mir Faizal
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Correspondence to Saurya Das.

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Das, S., Faizal, M. Dimensional reduction via a novel Higgs mechanism. Gen Relativ Gravit 50, 87 (2018). https://doi.org/10.1007/s10714-018-2409-x

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