Massive p-form trapping as a p-form on a brane

  • I. C. Jardim
  • G. Alencar
  • R. R. Landim
  • R. N. Costa Filho
Open Access
Regular Article - Theoretical Physics

Abstract

It is shown here that the zero mode of any form field can be trapped to the brane using the model proposed by Ghoroku and Nakamura. We start proven that the equations of motion can be obtained without splitting the field in even and odd parts. The massive and tachyonic cases are studied revealing that this mechanism only traps the zero mode. The result is then generalized to thick branes. In this scenario, the use of a delta like interaction of the quadratic term is necessary leading to a “mixed” potential with singular and smooth contributions. It is also shown that all forms produces an effective theory in the brane without gauge fixing. The existence of resonances with the transfer matrix method is then discussed. With this we analyze the resonances and look for peaks indicating the existence of unstable modes. Curiously no resonances are found in opposition of other models in the literature. Finally we find analytical solutions for arbitrary p-forms when a specific kind of smooth scenario is considered.

Keywords

p-branes Large Extra Dimensions Field Theories in Higher Dimensions 

Notes

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.

References

  1. [1]
    D. Bailin and A. Love, Kaluza-Klein theories, Rept. Prog. Phys. 50 (1987) 1087 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    A. Salam and J.A. Strathdee, On Kaluza-Klein Theory, Annals Phys. 141 (1982) 316 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    M. Gogberashvili, Our world as an expanding shell, Europhys. Lett. 49 (2000) 396 [hep-ph/9812365] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    I.C. Jardim, R.R. Landim, G. Alencar and R.N. Costa Filho, The construction of multiple spherical branes cosmological scenario, Phys. Rev. D 84 (2011) 064019 [arXiv:1105.4578] [INSPIRE].ADSGoogle Scholar
  5. [5]
    I.C. Jardim, R.R. Landim, G. Alencar and R.N. Costa Filho, Cosmologies of Multiple Spherical Brane-universe Model, Phys. Rev. D 88 (2013) 024004 [arXiv:1301.2578] [INSPIRE].ADSGoogle Scholar
  6. [6]
    K. Akama, T. Hattori and H. Mukaida, General Solution for the Static, Spherical and Asymptotically Flat Braneworld, arXiv:1109.0840 [INSPIRE].
  7. [7]
    L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    B. Bajc and G. Gabadadze, Localization of matter and cosmological constant on a brane in anti-de Sitter space, Phys. Lett. B 474 (2000) 282 [hep-th/9912232] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    A. Kehagias and K. Tamvakis, Localized gravitons, gauge bosons and chiral fermions in smooth spaces generated by a bounce, Phys. Lett. B 504 (2001) 38 [hep-th/0010112] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    G.R. Dvali and M.A. Shifman, Domain walls in strongly coupled theories, Phys. Lett. B 396 (1997) 64 [Erratum ibid. B 407 (1997) 452] [hep-th/9612128] [INSPIRE].
  12. [12]
    I. Oda, A new mechanism for trapping of photon, hep-th/0103052 [INSPIRE].
  13. [13]
    A.E.R. Chumbes, J.M. Hoff da Silva and M.B. Hott, A model to localize gauge and tensor fields on thick branes, Phys. Rev. D 85 (2012) 085003 [arXiv:1108.3821] [INSPIRE].ADSGoogle Scholar
  14. [14]
    G. Alencar, R.R. Landim, M.O. Tahim and R.N. Costa Filho, Gauge Field Localization on the Brane Through Geometrical Coupling, Phys. Lett. B 739 (2014) 125 [arXiv:1409.4396] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    G. Alencar, R.R. Landim, M.O. Tahim and R.N. Costa Filho, Gauge field emergence from Kalb-Ramond localization, Phys. Lett. B 742 (2015) 256 [arXiv:1409.5042] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  16. [16]
    I.C. Jardim, G. Alencar, R.R. Landim and R.N.C. Filho, Solutions to the problem of ELKO spinor localization in brane models, arXiv:1411.6962 [INSPIRE].
  17. [17]
    C. Germani, Spontaneous localization on a brane via a gravitational mechanism, Phys. Rev. D 85 (2012) 055025 [arXiv:1109.3718] [INSPIRE].ADSGoogle Scholar
  18. [18]
    K. Ghoroku and A. Nakamura, Massive vector trapping as a gauge boson on a brane, Phys. Rev. D 65 (2002) 084017 [hep-th/0106145] [INSPIRE].ADSMathSciNetGoogle Scholar
  19. [19]
    N. Kaloper, E. Silverstein and L. Susskind, Gauge symmetry and localized gravity in M-theory, JHEP 05 (2001) 031 [hep-th/0006192] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    M.J. Duff and P. van Nieuwenhuizen, Quantum Inequivalence of Different Field Representations, Phys. Lett. B 94 (1980) 179 [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    M.J. Duff and J.T. Liu, Hodge duality on the brane, Phys. Lett. B 508 (2001) 381 [hep-th/0010171] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    G. Alencar, M.O. Tahim, R.R. Landim, C.R. Muniz and R.N. Costa Filho, Bulk Antisymmetric tensor fields coupled to a dilaton in a Randall-Sundrum model, Phys. Rev. D 82 (2010) 104053 [arXiv:1005.1691] [INSPIRE].ADSGoogle Scholar
  23. [23]
    G. Alencar, R.R. Landim, M.O. Tahim, C.R. Muniz and R.N. Costa Filho, Antisymmetric Tensor Fields in Randall Sundrum Thick Branes, Phys. Lett. B 693 (2010) 503 [arXiv:1008.0678] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    G. Alencar, R.R. Landim, M.O. Tahim, K.C. Mendes and R.N. Costa Filho, Antisymmetric Tensor Fields in Codimension Two Brane-World, Europhys. Lett. 93 (2011) 10003 [arXiv:1009.1183] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    R.R. Landim, G. Alencar, M.O. Tahim, M.A.M. Gomes and R.N. Costa Filho, On resonances of q-forms in thick p-branes, Europhys. Lett. 97 (2012) 20003 [arXiv:1010.1548] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    G. Alencar, R.R. Landim, M.O. Tahim and R.N. Costa Filho, Bosonic fields in crystal manifold, Phys. Lett. B 726 (2013) 809 [arXiv:1301.2562] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  27. [27]
    C.-E. Fu, Y.-X. Liu, K. Yang and S.-W. Wei, q-Form fields on p-branes, JHEP 10 (2012) 060 [arXiv:1207.3152] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    D. Bazeia and L. Losano, Deformed defects with applications to braneworlds, Phys. Rev. D 73 (2006) 025016 [hep-th/0511193] [INSPIRE].ADSMathSciNetGoogle Scholar
  29. [29]
    D. Bazeia, F.A. Brito and A.R. Gomes, Locally localized gravity and geometric transitions, JHEP 11 (2004) 070 [hep-th/0411088] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    D. Bazeia, J. Menezes and R. Menezes, New global defect structures, Phys. Rev. Lett. 91 (2003) 241601 [hep-th/0305234] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    Y.-X. Liu, J. Yang, Z.-H. Zhao, C.-E. Fu and Y.-S. Duan, Fermion Localization and Resonances on A de Sitter Thick Brane, Phys. Rev. D 80 (2009) 065019 [arXiv:0904.1785] [INSPIRE].ADSGoogle Scholar
  32. [32]
    Z.-H. Zhao, Y.-X. Liu and H.-T. Li, Fermion localization on asymmetric two-field thick branes, Class. Quant. Grav. 27 (2010) 185001 [arXiv:0911.2572] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  33. [33]
    J. Liang and Y.-S. Duan, Localization of matter and fermion resonances on double walls, Phys. Lett. B 681 (2009) 172 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    Z.-H. Zhao, Y.-X. Liu, H.-T. Li and Y.-Q. Wang, Effects of the variation of mass on fermion localization and resonances on thick branes, Phys. Rev. D 82 (2010) 084030 [arXiv:1004.2181] [INSPIRE].ADSGoogle Scholar
  35. [35]
    Z.-H. Zhao, Y.-X. Liu, Y.-Q. Wang and H.-T. Li, Effects of temperature on thick branes and the fermion (quasi-)localization, JHEP 06 (2011) 045 [arXiv:1102.4894] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  36. [36]
    A. Ahmed, B. Grzadkowski and J. Wudka, Thick-Brane Cosmology, JHEP 04 (2014) 061 [arXiv:1312.3576] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    H. Guo, Y.-X. Liu, Z.-H. Zhao and F.-W. Chen, Thick branes with a non-minimally coupled bulk-scalar field, Phys. Rev. D 85 (2012) 124033 [arXiv:1106.5216] [INSPIRE].ADSGoogle Scholar
  38. [38]
    V. Dzhunushaliev, V. Folomeev and M. Minamitsuji, Thick brane solutions, Rept. Prog. Phys. 73 (2010) 066901 [arXiv:0904.1775] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  39. [39]
    M.S. Movahed and S. Ghassemi, Is Thick Brane Model Consistent with the Recent Observations?, Phys. Rev. D 76 (2007) 084037 [arXiv:0705.3894] [INSPIRE].ADSGoogle Scholar
  40. [40]
    Y.-Z. Du, L. Zhao, Y. Zhong, C.-E. Fu and H. Guo, Resonances of Kalb-Ramond field on symmetric and asymmetric thick branes, Phys. Rev. D 88 (2013) 024009 [arXiv:1301.3204] [INSPIRE].ADSGoogle Scholar
  41. [41]
    M. Gremm, Four-dimensional gravity on a thick domain wall, Phys. Lett. B 478 (2000) 434 [hep-th/9912060] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    D. Bazeia and A.R. Gomes, Bloch brane, JHEP 05 (2004) 012 [hep-th/0403141] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    D. Bazeia, F.A. Brito and L. Losano, Scalar fields, bent branes and RG flow, JHEP 11 (2006) 064 [hep-th/0610233] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  44. [44]
    C. Csáki, J. Erlich, T.J. Hollowood and Y. Shirman, Universal aspects of gravity localized on thick branes, Nucl. Phys. B 581 (2000) 309 [hep-th/0001033] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  45. [45]
    R.R. Landim, G. Alencar, M.O. Tahim and R.N. Costa Filho, A Transfer Matrix Method for Resonances in Randall-Sundrum Models, JHEP 08 (2011) 071 [arXiv:1105.5573] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  46. [46]
    R.R. Landim, G. Alencar, M.O. Tahim and R.N. Costa Filho, A Transfer Matrix Method for Resonances in Randall-Sundrum Models II: The Deformed Case, JHEP 02 (2012) 073 [arXiv:1110.5855] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  47. [47]
    M. Cvetič and M. Robnik, Gravity Trapping on a Finite Thickness Domain Wall: An Analytic Study, Phys. Rev. D 77 (2008) 124003 [arXiv:0801.0801] [INSPIRE].ADSGoogle Scholar
  48. [48]
    G. Alencar, R.R. Landim, M.O. Tahim and R.N.C. Filho, A Transfer Matrix Method for Resonances in Randall-Sundrum Models III: An analytical comparison, JHEP 01 (2013) 050 [arXiv:1207.3054] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  49. [49]
    R.R. Landim, G. Alencar, M.O. Tahim and R.N. Costa Filho, New Analytical Solutions for Bosonic Field Trapping in Thick Branes, Phys. Lett. B 731 (2014) 131 [arXiv:1310.2147] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  50. [50]
    A. Melfo, N. Pantoja and A. Skirzewski, Thick domain wall space-times with and without reflection symmetry, Phys. Rev. D 67 (2003) 105003 [gr-qc/0211081] [INSPIRE].ADSGoogle Scholar
  51. [51]
    G. Alencar, R.R. Landim, C.R. Muniz and R.N.C. Filho, Non-minimal couplings in Randall-Sundrum Scenarios, arXiv:1502.02998 [INSPIRE].
  52. [52]
    G. ’t Hooft, Renormalizable Lagrangians for Massive Yang-Mills Fields, Nucl. Phys. B 35 (1971) 167 [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • I. C. Jardim
    • 1
  • G. Alencar
    • 1
  • R. R. Landim
    • 1
  • R. N. Costa Filho
    • 1
  1. 1.Departamento de FísicaUniversidade Federal do Ceará- Caixa Postal 6030FortalezaBrazil

Personalised recommendations