Skip to main content

Covert symmetry breaking

A preprint version of the article is available at arXiv.

Abstract

Reduction from a higher-dimensional to a lower-dimensional field theory can display special features when the zero-level ground state has nontrivial dependence on the reduction coordinates. In particular, a delayed ‘covert’ form of spontaneous symmetry breaking can occur, revealing itself only at fourth order in the lower-dimensional effective field theory action. This phenomenon is explored in a simple model of (d + 1)-dimensional scalar QED with one dimension restricted to an interval with Dirichlet/Robin boundary conditions on opposing ends. This produces an effective d-dimensional theory with Maxwellian dynamics at the free theory level, but with unusual symmetry breaking appearing in the quartic vector-scalar interaction terms. This simple model is chosen to illuminate the mechanism of effects which are also noted in gravitational braneworld scenarios.

References

  1. [1]

    R.L. Arnowitt, S. Deser and C.W. Misner, The Dynamics of general relativity, Gen. Rel. Grav. 40 (2008) 1997 [gr-qc/0405109] [INSPIRE].

    ADS  Article  Google Scholar 

  2. [2]

    R. Feynman, F. Morinigo, W. Wagner and B. Hatfield, Feynman lectures on gravitation, Addison-Wesley (1995) [INSPIRE].

  3. [3]

    S. Weinberg, Photons and gravitons in perturbation theory: Derivation of Maxwell’s and Einstein’s equations, Phys. Rev. 138 (1965) B988 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  4. [4]

    S. Deser, Selfinteraction and gauge invariance, Gen. Rel. Grav. 1 (1970) 9 [gr-qc/0411023] [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    D.Z. Freedman, P. van Nieuwenhuizen and S. Ferrara, Progress Toward a Theory of Supergravity, Phys. Rev. D 13 (1976) 3214 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  6. [6]

    S. Deser and B. Zumino, Consistent Supergravity, Phys. Lett. B 62 (1976) 335 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  7. [7]

    P.G.O. Freund and M.A. Rubin, Dynamics of Dimensional Reduction, Phys. Lett. B 97 (1980) 233 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  8. [8]

    M.J. Duff, B.E.W. Nilsson, C.N. Pope and N.P. Warner, On the Consistency of the {Kaluza-Klein} Ansatz, Phys. Lett. B 149 (1984) 90 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  9. [9]

    B. de Wit, H. Nicolai and N.P. Warner, The Embedding of Gauged N = 8 Supergravity Into d = 11 Supergravity, Nucl. Phys. B 255 (1985) 29 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  10. [10]

    B. de Wit and H. Nicolai, The Consistency of the S7 Truncation in D = 11 Supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  11. [11]

    M.J. Duff and C.N. Pope, Consistent truncations in Kaluza-Klein theories, Nucl. Phys. B 255 (1985) 355 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  12. [12]

    H. Godazgar, M. Godazgar, O. Krüger and H. Nicolai, Consistent 4-form fluxes for maximal supergravity, JHEP 10 (2015) 169 [arXiv:1507.07684] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  13. [13]

    M.J. Duff, S. Ferrara, C.N. Pope and K.S. Stelle, Massive Kaluza-Klein Modes and Effective Theories of Superstring Moduli, Nucl. Phys. B 333 (1990) 783 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  14. [14]

    B. Crampton, C.N. Pope and K.S. Stelle, Braneworld localisation in hyperbolic spacetime, JHEP 12 (2014) 035 [arXiv:1408.7072] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  15. [15]

    M. Cvetič, G.W. Gibbons and C.N. Pope, A String and M-theory origin for the Salam-Sezgin model, Nucl. Phys. B 677 (2004) 164 [hep-th/0308026] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  16. [16]

    S. Deser and K.S. Stelle, Field redefinition’s help in constructing non-abelian gauge theories, Phys. Lett. B 798 (2019) 135007 [arXiv:1908.05511] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  17. [17]

    K.S. Stelle, Mass gaps and braneworlds, J. Phys. A 53 (2020) 204002 [arXiv:2004.00965] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  18. [18]

    C. Erickson, A. Harrold, R. Leung and K.S. Stelle, in preparation.

  19. [19]

    C.M. Hull and N.P. Warner, Noncompact Gaugings From Higher Dimensions, Class. Quant. Grav. 5 (1988) 1517 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  20. [20]

    D. Brecher and M.J. Perry, Ricci flat branes, Nucl. Phys. B 566 (2000) 151 [hep-th/9908018] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  21. [21]

    A. Chamblin, S.W. Hawking and H.S. Reall, Brane world black holes, Phys. Rev. D 61 (2000) 065007 [hep-th/9909205] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  22. [22]

    H. Lü and C.N. Pope, Branes on the brane, Nucl. Phys. B 598 (2001) 492 [hep-th/0008050] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to K. S. Stelle.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2007.12192

Rights and permissions

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.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Erickson, C.W., Harrold, A.D., Leung, R. et al. Covert symmetry breaking. J. High Energ. Phys. 2020, 157 (2020). https://doi.org/10.1007/JHEP10(2020)157

Download citation

Keywords

  • Brane Dynamics in Gauge Theories
  • Effective Field Theories
  • Gauge Symmetry
  • Spontaneous Symmetry Breaking