Skip to main content
Log in

Introduction to localization of Elko spinor fields on branes

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

In 2004, Dharam Vir Ahluwalia and Daniel Grumiller discovered a dark matter candidate called Elko: spin one-half fermions with mass dimension one. These fermions are described by a spinorial Klein-Gordon formalism and very different from electrons or neutrinos. In this review, we give a brief introduction to the localization of Elko spinor fields on branes. First, we briefly review some brane-world theories and the localization of bulk matter fields on branes. Then, after a brief introduction to Elko spinor fields, we focus on the localization of Elko fields on branes in three cases: the free Elko fields, the Elko fields with Yukawa-like coupling, and finally, the Elko fields with non-minimal coupling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T. Kaluza, Sitzungsber. Preuss. Akad. Wiss. Berlin. (Math. Phys.) 96, 966C972 (1921)

    Google Scholar 

  2. O. Klein, Z. Phys. A 37, 895C906 (1926)

    Google Scholar 

  3. N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali, Phys. Lett. B 429, 263 (1998)

    ADS  Google Scholar 

  4. L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999)

    ADS  MathSciNet  Google Scholar 

  5. L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  7. V.A. Rubakov, M.E. Shaposhnikov, Phys. Lett. B 125, 139 (1983)

    ADS  Google Scholar 

  8. I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali, Phys. Lett. B 436, 257 (1998)

    ADS  Google Scholar 

  9. S. Das, D. Maity, S. SenGupta, JHEP 0805, 042 (2008)

    ADS  Google Scholar 

  10. K. Yang, Y.X. Liu, Y. Zhong, X.L. Du, S.W. Wei, Phys. Rev. D 86, 127502 (2012)

    ADS  Google Scholar 

  11. B. Guo, Y.X. Liu, K. Yang, S.W. Wei, Phys. Rev. D 98, 085022 (2018)

    ADS  MathSciNet  Google Scholar 

  12. N. Arkani-Hamed, S. Dimopoulos, N. Kaloper, R. Sundrum, Phys. Lett. B 480, 193 (2000)

    ADS  MathSciNet  Google Scholar 

  13. J.E. Kim, B. Kyae, H.M. Lee, Phys. Rev. Lett. 86, 4223 (2001)

    ADS  MathSciNet  Google Scholar 

  14. G.D. Starkman, D. Stojkovic, M. Trodden, Phys. Rev. D 63, 103511 (2001)

    ADS  Google Scholar 

  15. G.D. Starkman, D. Stojkovic, M. Trodden, Phys. Rev. Lett. 87, 231303 (2001)

    ADS  MathSciNet  Google Scholar 

  16. A. Kehagias, Phys. Lett. B 600, 133 (2004)

    ADS  MathSciNet  Google Scholar 

  17. D.P. George, M. Trodden, R.R. Volkas, JHEP 0902, 035 (2009)

    ADS  Google Scholar 

  18. P. Dey, B. Mukhopadhyaya, S. SenGupta, Phys. Rev. D 80, 055029 (2009)

    ADS  Google Scholar 

  19. Z. Haghani, H.R. Sepangi, S. Shahidi, JCAP 1202, 031 (2012)

    ADS  Google Scholar 

  20. N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali, Phys. Rev. D 59, 086004 (1999)

    ADS  Google Scholar 

  21. V. Sahni, Y. Shtanov, JCAP 0311, 014 (2003)

    ADS  Google Scholar 

  22. J.A.R. Cembranos, A. Dobado, A.L. Maroto, Phys. Rev. Lett. 90, 241301 (2003)

    ADS  Google Scholar 

  23. T. Nihei, N. Okada, O. Seto, Phys. Rev. D 71, 063535 (2005)

    ADS  Google Scholar 

  24. C.D. Hoyle, U. Schmidt, B.R. Heckel, E.G. Adelberger, J.H. Gundlach, D.J. Kapner, H.E. Swanson, Phys. Rev. Lett. 86, 1418 (2001)

    ADS  Google Scholar 

  25. P.Q. Hung, N.K. Tran, Phys. Rev. D 69, 064003 (2004)

    ADS  MathSciNet  Google Scholar 

  26. E.G. Adelberger, B.R. Heckel, S.A. Hoedl, C.D. Hoyle, D.J. Kapner, A. Upadhye, Phys. Rev. Lett. 98, 131104 (2007)

    ADS  Google Scholar 

  27. M. Gremm, Phys. Lett. B 478, 434 (2000)

    ADS  Google Scholar 

  28. O. DeWolfe, D.Z. Freedman, S.S. Gubser, A. Karch, Phys. Rev. D 62, 046008 (2000)

    ADS  MathSciNet  Google Scholar 

  29. S. Kobayashi, K. Koyama, J. Soda, Phys. Rev. D 65, 064014 (2002)

    ADS  MathSciNet  Google Scholar 

  30. D. Bazeia, L. Losano, C. Wotzasek, Phys. Rev. D 66, 105025 (2002)

    ADS  Google Scholar 

  31. A. Wang, Phys. Rev. D 66, 024024 (2002)

    ADS  MathSciNet  Google Scholar 

  32. A. Melfo, N. Pantoja, A. Skirzewski, Phys. Rev. D 67, 105003 (2003)

    ADS  MathSciNet  Google Scholar 

  33. D. Bazeia, A.R. Gomes, JHEP 0405, 012 (2004)

    ADS  Google Scholar 

  34. V.I. Afonso, D. Bazeia, L. Losano, Phys. Lett. B 634, 526 (2006)

    ADS  MathSciNet  Google Scholar 

  35. D. Bazeia, F.A. Brito, L. Losano, JHEP 0611, 064 (2006)

    ADS  Google Scholar 

  36. C. Bogdanos, A. Dimitriadis, K. Tamvakis, Phys. Rev. D 74, 045003 (2006)

    ADS  MathSciNet  Google Scholar 

  37. V. Dzhunushaliev, V. Folomeev, M. Minamitsuji, Rep. Prog. Phys. 73, 066901 (2010)

    ADS  Google Scholar 

  38. Y.X. Liu, Y. Zhong, K. Yang, Europhys. Lett. 90, 51001 (2010)

    ADS  Google Scholar 

  39. Y.X. Liu, K. Yang, Y. Zhong, JHEP 1010, 069 (2010)

    ADS  Google Scholar 

  40. Y.X. Liu, Y. Zhong, Z.H. Zhao, H.T. Li, JHEP 1106, 135 (2011)

    ADS  Google Scholar 

  41. H. Guo, Y.X. Liu, Z.H. Zhao, F.W. Chen, Phys. Rev. D 85, 124033 (2012)

    ADS  Google Scholar 

  42. Y.X. Liu, K. Yang, H. Guo, Y. Zhong, Phys. Rev. D 85, 124053 (2012)

    ADS  Google Scholar 

  43. Y.X. Liu, F.W. Chen, Heng-Guo, X.N. Zhou, JHEP 1205, 108 (2012)

    ADS  Google Scholar 

  44. D. Bazeia, F.A. Brito, F.G. Costa, Phys. Rev. D 87, 065007 (2013)

    ADS  Google Scholar 

  45. G. German, A. Herrera-Aguilar, D. Malagon–Morejon, I. Quiros, R. da Rocha, Phys. Rev. D 89, 026004 (2014)

    ADS  Google Scholar 

  46. A. de Souza Dutra, G.P. de Brito, J.M. Hoff da Silva, Phys. Rev. D 91, 086016 (2015)

    ADS  MathSciNet  Google Scholar 

  47. B. Guo, Y.X. Liu, K. Yang, Eur. Phys. J. C 75, 63 (2015)

    ADS  Google Scholar 

  48. W.J. Geng, H. Lu, Phys. Rev. D 93, 044035 (2016)

    ADS  MathSciNet  Google Scholar 

  49. N. Barbosa-Cendejas, A. Herrera-Aguilar, JHEP 0510, 101 (2005)

    ADS  Google Scholar 

  50. A. Herrera-Aguilar, D. Malagon-Morejon, R.R. Mora-Luna, JHEP 1011, 015 (2010)

    ADS  Google Scholar 

  51. Y. Zhong, Y.X. Liu, Eur. Phys. J. C 76, 321 (2016)

    ADS  Google Scholar 

  52. Y.X. Liu, Introduction to extra dimensions and thick brane worlds

  53. B. Bajc, G. Gabadadze, Phys. Lett. B 474, 282 (2000)

    ADS  MathSciNet  Google Scholar 

  54. T. Gherghetta, M.E. Shaposhnikov, Phys. Rev. Lett. 85, 240 (2000)

    ADS  MathSciNet  Google Scholar 

  55. I. Oda, Phys. Lett. B 496, 113 (2000)

    ADS  Google Scholar 

  56. Y.X. Liu, L.D. Zhang, S.W. Wei, Y.S. Duan, JHEP 0808, 041 (2008)

    ADS  Google Scholar 

  57. Y.-X. Liu, Z.-H. Zhao, S.-W. Wei, Y.-S. Duan, JCAP 0902, 003 (2009)

    ADS  Google Scholar 

  58. R. Guerrero, A. Melfo, N. Pantoja, R.O. Rodriguez, Phys. Rev. D 81, 086004 (2010)

    ADS  Google Scholar 

  59. A.E.R. Chumbes, J.M.H. da Silva, M.B. Hott, Phys. Rev. D 85, 085003 (2012)

    ADS  Google Scholar 

  60. W.T. Cruz, A.R.P. Lima, C.A.S. Almeida, Phys. Rev. D 87, 045018 (2013)

    ADS  Google Scholar 

  61. Z.H. Zhao, Y.X. Liu, Y. Zhong, Phys. Rev. D 90, 045031 (2014)

    ADS  Google Scholar 

  62. G. Alencar, R.R. Landim, M.O. Tahim, R.N. Costa Filho, Phys. Lett. B 739, 125 (2014)

    ADS  MathSciNet  Google Scholar 

  63. C.A. Vaquera-Araujo, O. Corradini, Eur. Phys. J. C 75, 48 (2015)

    ADS  Google Scholar 

  64. Y.Z. Du, L. Zhao, Y. Zhong, C.E. Fu, H. Guo, Phys. Rev. D 88, 024009 (2013)

    ADS  Google Scholar 

  65. C.E. Fu, Y.X. Liu, H. Guo, F.W. Chen, S.L. Zhang, Phys. Lett. B 735, 7 (2014)

    ADS  MathSciNet  Google Scholar 

  66. C.E. Fu, Y.X. Liu, H. Guo, S.L. Zhang, Phys. Rev. D 93, 064007 (2016)

    ADS  MathSciNet  Google Scholar 

  67. C.E. Fu, Y. Zhong, Q.Y. Xie, Y.X. Liu, Phys. Lett. B 757, 180 (2016)

    ADS  Google Scholar 

  68. Y.X. Liu, L.-D. Zhang, L.-J. Zhang, Y.-S. Duan, Phys. Rev. D. 78, 065025 (2008)

    ADS  MathSciNet  Google Scholar 

  69. H. Guo, A. Herrera-Aguilar, Y.X. Liu, D. Malagon-Morejon, R.R. Mora-Luna, Phys. Rev. D 87, 095011 (2013)

    ADS  Google Scholar 

  70. Y.X. Liu, X.H. Zhang, L.D. Zhang, Y.S. Duan, JHEP 0802, 067 (2008)

    ADS  Google Scholar 

  71. Y.X. Liu, H. Guo, C.E. Fu, J.R. Ren, JHEP 1002, 080 (2010)

    ADS  Google Scholar 

  72. Z.H. Zhao, Y.X. Liu, H.T. Li, Y.Q. Wang, Phys. Rev. D 82, 084030 (2010)

    ADS  Google Scholar 

  73. A.E.R. Chumbes, A.E.O. Vasquez, M.B. Hott, Phys. Rev. D 83, 105010 (2011)

    ADS  Google Scholar 

  74. Y.X. Liu, H. Guo, C.E. Fu, H.T. Li, Phys. Rev. D 84, 044033 (2011)

    ADS  Google Scholar 

  75. C. Germani, Phys. Rev. D 85, 055025 (2012)

    ADS  Google Scholar 

  76. Y.X. Liu, Z.G. Xu, F.W. Chen, S.W. Wei, Phys. Rev. D 89, 086001 (2014)

    ADS  Google Scholar 

  77. Y.P. Zhang, Y.Z. Du, W.D. Guo, Y.X. Liu, Phys. Rev. D 93, 065042 (2016)

    ADS  MathSciNet  Google Scholar 

  78. Y.Y. Li, Y.P. Zhang, W.D. Guo, Y.X. Liu, Phys. Rev. D 95, 115003 (2017)

    ADS  Google Scholar 

  79. Y.Z. Du, L. Zhao, X.N. Zhou, Y. Zhong, Y.X. Liu, Ann. Phys. 388, 69 (2018)

    ADS  Google Scholar 

  80. X.N. Zhou, Y.Z. Du, H. Yu, Y.X. Liu, Sci. China Phys. Mech. Astron. 61, 110411 (2018)

    ADS  Google Scholar 

  81. D.V. Ahluwalia, D. Grumiller, Phys. Rev. D 72, 067701 (2005)

    ADS  Google Scholar 

  82. D.V. Ahluwalia, D. Grumiller, JCAP 0507, 012 (2005)

    ADS  Google Scholar 

  83. D.V. Ahluwalia, C.Y. Lee, D. Schritt, Phys. Lett. B 687, 248 (2010)

    ADS  Google Scholar 

  84. D.V. Ahluwalia, C.Y. Lee, D. Schritt, Phys. Rev. D 83, 065017 (2011)

    ADS  Google Scholar 

  85. D.V. Ahluwalia-Khalilova, S.P. Horvath, JHEP 1011, 078 (2010)

    ADS  Google Scholar 

  86. A. Alves, M. Dias, F. de Campos, L. Duarte, J.M.H. da Silva, Europhys. Lett. 121, 31001 (2018)

    ADS  Google Scholar 

  87. M. Dias, F. de Campos, J.M.H. da Silva, Phys. Lett. B 706, 352 (2012)

    ADS  Google Scholar 

  88. C.Y. Lee, Int. J. Mod. Phys. A 30, 1550048 (2015)

    ADS  Google Scholar 

  89. C.Y. Lee, Int. J. Mod. Phys. A 31, 1650187 (2016)

    ADS  Google Scholar 

  90. L. Fabbri, Gen. Relativ. Gravit. 43, 1607 (2011)

    ADS  Google Scholar 

  91. C.G. Boehmer, Phys. Rev. D 77, 123535 (2008)

    ADS  Google Scholar 

  92. C.G. Boehmer, J. Burnett, Phys. Rev. D 78, 104001 (2008)

    ADS  Google Scholar 

  93. C.G. Boehmer, J. Burnett, D.F. Mota, D.J. Shaw, JHEP 1007, 053 (2010)

    ADS  Google Scholar 

  94. H. Wei, Phys. Lett. B 695, 307 (2011)

    ADS  Google Scholar 

  95. D. Gredat, S. Shankaranarayanan, JCAP 1001, 008 (2010)

    ADS  Google Scholar 

  96. A. Basak, S. Shankaranarayanan, JCAP 1505, 034 (2015)

    ADS  Google Scholar 

  97. S.H. Pereira, A.P.S.S., J.M.H. da Silva, JCAP 1408, 020 (2014)

    ADS  Google Scholar 

  98. S.H. Pereira, A.P.S.S., J.M.H. da Silva, J.F. Jesus, JCAP 1701, 055 (2017)

    ADS  Google Scholar 

  99. S.H. Pereira, T.M. Guimarães, JCAP 09, 038 (2017)

    ADS  Google Scholar 

  100. S.H. Pereira, Europhys. Lett. 120, 31001 (2017)

    ADS  Google Scholar 

  101. S.H. Pereira, R.S. Costa, Mod. Phys. Lett. A 34, 1950126 (2019)

    ADS  Google Scholar 

  102. R.V. Maluf, D.M. Dantas, C.A.S. Almeida, Eur. Phys. J. C 80, 442 (2020)

    ADS  Google Scholar 

  103. J.M.H. da Silva, R. da Rocha, Int. J. Mod. Phys. A 24, 3227 (2009)

    ADS  Google Scholar 

  104. J.M. Hoff da Silva, C.H. Coronado Villalobos, R.J. Bueno Rogerio, E. Scatena, Eur. Phys. J. C 76, 563 (2016)

    ADS  Google Scholar 

  105. J.A. Nieto, Rev. Mex. Fis. 60, 371 (2014)

    Google Scholar 

  106. R. da Rocha, A.E. Bernardini, J.M. Hoff da Silva, JHEP 1104, 110 (2011)

    ADS  Google Scholar 

  107. R. Abłamowicz, I. Gonçalves, R. da Rocha, J. Math. Phys. 55, 103501 (2014)

    ADS  MathSciNet  Google Scholar 

  108. R.J. Bueno Rogerio, J.M.H. da Silva, S.H. Pereira, R. da Rocha, Europhys. Lett. 113, 60001 (2016)

    ADS  Google Scholar 

  109. R.T. Cavalcanti, Int. J. Mod. Phys. D 23, 1444002 (2014)

    ADS  Google Scholar 

  110. R.T. Cavalcanti, J.M.H. da Silva, R. da Rocha, Eur. Phys. J. Plus 129, 246 (2014)

    Google Scholar 

  111. Luca Fabbri, Adv. Appl. Clifford Algebras 28, 7 (2018)

    Google Scholar 

  112. C.Y. Lee,Mass dimension one fermions from flag dipole spinors, arXiv:1809.04381 [hep-th] (2018)

  113. D.V. Ahluwalia, S. Sarmah, Europhys. Lett. 125, 30005 (2019)

    Google Scholar 

  114. J.A. Nieto, Mod. Phys. Lett. A 34, 1950211 (2019)

    ADS  Google Scholar 

  115. C.H. Coronado Villalobos, R.J. Bueno Rogerio, E.F.T. São Sabbas, Eur. Phys. J. C 79, 308 (2019) [Erratum: Eur. Phys. J. C 79, 587 (2019)]

    ADS  Google Scholar 

  116. D.V. Ahluwalia,Mass dimension one fermions (Cambridge University Press, 2019)

  117. Y.X. Liu, X.N. Zhou, K. Yang, F.W. Chen, Phys. Rev. D 86, 064012 (2012)

    ADS  Google Scholar 

  118. I.C. Jardim, G. Alencar, R.R. Landim, R.N. Costa Filho, Phys. Rev. D 91, 048501 (2015)

    ADS  Google Scholar 

  119. I.C. Jardim, G. Alencar, R.R. Landim, R.N. Costa Filho, Phys. Rev. D 91, 085008 (2015)

    ADS  MathSciNet  Google Scholar 

  120. X.N. Zhou, Localization of Elko field on brane world and qusibound states around black hole, Ph.D. thesis, Lanzhou University, Institute of Theoretical Physics, 2015

  121. D.M. Dantas, R. da Rocha, C.A.S. Almeida, Europhys. Lett. 117, 51001 (2017)

    ADS  Google Scholar 

  122. X.N. Zhou, Y.Z. Du, Z.H. Zhao, Y.X. Liu, Eur. Phys. J. C 78, 493 (2018)

    ADS  Google Scholar 

  123. X.N. Zhou, X.Y. Ma, Z.H. Zhao, Y.Z. Du,Localization of five-dimensional Elko spinors on dS/AdS thick branes, arXiv:1812.08332 [hep-th]

  124. M.M. Sorkhi, Z. Ghalenovi, Int. J. Mod. Phys. A 33, 1850172 (2018)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu-Xiao Liu.

Additional information

Publisher's Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, XN., Liu, YX. Introduction to localization of Elko spinor fields on branes. Eur. Phys. J. Spec. Top. 229, 2043–2078 (2020). https://doi.org/10.1140/epjst/e2020-900274-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2020-900274-4

Navigation