Skip to main content
SpringerLink
Log in

A transfer matrix method for resonances in Randall-Sundrum models

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

In this paper we discuss in detail a numerical method to study resonances in membranes generated by domain walls in Randall-Sundrum-like scenarios. It is based on similar works to understand the quantum mechanics of electrons subject to the potential barriers that exist in heterostructures in semiconductors. This method was used recently to study resonances of a three form field and lately generalized to arbitrary forms. We apply it to a lot of important models, namely those that contain the Gauge, Gravity and Spinor fields. In many cases we find a rich structure of resonances which depends on the parameters involved.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Kim and G.B. Arnold, Theoretical study of tunneling phenomena in double-barrier quantum-well heterostructures, Phys. Rev. B 38 (1988) 3252.

    ADS  Google Scholar 

  2. R. Renan, V.N. Freire, M.M. Auto and G.A. Farias, Transmission coefficient of electrons through a single graded barrier, Phys. Rev. B 49 (1993) 8446.

    ADS  Google Scholar 

  3. R.R. L. de Carvalho, V.N. Freire, M.M. Auto and G. A. Farias, Transmission in symmetrical GaAs/Al x Ga 1−x As double barrier with compositionally nonabrupt interfaces, Superlat. Microstruct. 15 (1994) 203.

    Article  ADS  Google Scholar 

  4. Y. Ando and T. Itoh, Calculation of transmission tunneling current across arbitrary potential barriers, J. Appl. Phys. 61 (1987) 1497.

    Article  ADS  Google Scholar 

  5. L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

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

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. B. Mukhopadhyaya, S. Sen, S. Sen and S. SenGupta, Bulk Kalb-Ramond field in Randall Sundrum scenario, Phys. Rev. D 70 (2004) 066009 [hep-th/0403098] [SPIRES].

    ADS  Google Scholar 

  8. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String Axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [SPIRES].

    ADS  Google Scholar 

  9. P. Svrček and E. Witten, Axions in string theory, JHEP 06 (2006) 051 [hep-th/0605206] [SPIRES].

    Article  ADS  Google Scholar 

  10. J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge University Press, Cambridge U.K. (1998) SPIRES.

    Book  Google Scholar 

  11. J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge University Press, Cambridge U.K. (1998) [SPIRES].

    Book  Google Scholar 

  12. C. Germani and A. Kehagias, Higher-spin fields in braneworlds, Nucl. Phys. B 725 (2005) 15 [hep-th/0411269] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  13. B. Mukhopadhyaya, S. Sen and S. SenGupta, Bulk antisymmetric tensor fields in a Randall-Sundrum model, Phys. Rev. D 76 (2007) 121501 [arXiv:0709.3428] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  14. G. De Risi, Bouncing cosmology from Kalb-Ramond Braneworld, Phys. Rev. D 77 (2008) 044030 [arXiv:0711.3781] [SPIRES].

    ADS  Google Scholar 

  15. B. Mukhopadhyaya, S. Sen and S. SenGupta, A Randall-Sundrum scenario with bulk dilaton and torsion, Phys. Rev. D 79 (2009) 124029 [arXiv:0903.0722] [SPIRES].

    ADS  Google Scholar 

  16. 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] [SPIRES].

    ADS  Google Scholar 

  17. M. Gremm, Four-dimensional gravity on a thick domain wall, Phys. Lett. B 478 (2000) 434 [hep-th/9912060] [SPIRES].

    ADS  Google Scholar 

  18. Y. Brihaye, T. Delsate, N. Sawado and Y. Kodama, Inflating baby-Skyrme branes in six dimensions, Phys. Rev. D 82 (2010) 106002 [arXiv:1007.0736] [SPIRES].

    ADS  Google Scholar 

  19. Y. Brihaye and T. Delsate, Inflating brane inside hyper-spherically symmetric defects, Class. Quant. Grav. 24 (2007) 1279 [gr-qc/0605039] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  20. Y. Brihaye, T. Delsate and B. Hartmann, Inflating branes inside abelian strings, Phys. Rev. D 74 (2006) 044015 [hep-th/0602172] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  21. Y. Brihaye and T. Delsate, Remarks on bell-shaped lumps: stability and fermionic modes, Phys. Rev. D 78 (2008) 025014 [arXiv:0803.1458] [SPIRES].

    ADS  Google Scholar 

  22. D. Bazeia, A.R. Gomes, L. Losano and R. Menezes, Braneworld Models of Scalar Fields with Generalized Dynamics, Phys. Lett. B 671 (2009) 402 [arXiv:0808.1815] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  23. D. Bazeia, A.R. Gomes and L. Losano, Gravity localization on thick branes: a numerical approach, Int. J. Mod. Phys. A 24 (2009) 1135 [arXiv:0708.3530] [SPIRES].

    ADS  Google Scholar 

  24. D. Bazeia, F.A. Brito and A.R. Gomes, Locally localized gravity and geometric transitions, JHEP 11 (2004) 070 [hep-th/0411088] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  25. D. Bazeia, C. Furtado and A.R. Gomes, Brane structure from scalar field in warped spacetime, JCAP 02 (2004) 002 [hep-th/0308034] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  26. H.R. Christiansen, M.S. Cunha and M.O. Tahim, Exact solutions for a Maxwell-Kalb-Ramond action with dilaton: Localization of massless and massive modes in a sine-Gordon brane-world, Phys. Rev. D 82 (2010) 085023 [arXiv:1006.1366] [SPIRES].

    ADS  Google Scholar 

  27. 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] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  28. 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] [SPIRES].

    ADS  Google Scholar 

  29. R.R. Landim, G. Alencar, M.O. Tahim, M.A.M. Gomes and R.N.C. Filho, Dual Spaces of Resonance In Thick p − Branes, arXiv:1010.1548 [SPIRES].

  30. G. Alencar et al., Antisymmetric Tensor Fields in Codimension Two Brane-World, Europhys. Lett. 93 (2011) 10003 [arXiv:1009.1183] [SPIRES].

    Article  ADS  Google Scholar 

  31. D. Bazeia and L. Losano, Other results for deformed defects, Phys. Rev. D 73 (2006) 025016 [hep-th/0511193] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  32. D. Bazeia, L. Losano and J.M.C. Malbouisson, Deformed defects, Phys. Rev. D 66 (2002) 101701 [hep-th/0209027] [SPIRES].

    ADS  Google Scholar 

  33. 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] [SPIRES].

    ADS  Google Scholar 

  34. 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] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  35. J. Liang and Y.-S. Duan, Localization of matter and fermion resonances on double walls, Phys. Lett. B 681 (2009) 172 [SPIRES].

    ADS  Google Scholar 

  36. 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] [SPIRES].

    ADS  Google Scholar 

  37. 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] [SPIRES].

    Article  ADS  Google Scholar 

  38. H.-T. Li, Y.-X. Liu, Z.-H. Zhao and H. Guo, Fermion Resonances on a Thick Brane with a Piecewise Warp Factor, Phys. Rev. D 83 (2011) 045006 [arXiv:1006.4240] [SPIRES].

    ADS  Google Scholar 

  39. L.B. Castro, Fermion localization on two-field thick branes, Phys. Rev. D 83 (2011) 045002 [arXiv:1008.3665] [SPIRES].

    ADS  Google Scholar 

  40. R.A.C. Correa, A. de Souza Dutra and M.B. Hott, Fermion localization on degenerate and critical branes, Class. Quant. Grav. 28 (2011) 155012 [arXiv:1011.1849] [SPIRES].

    Article  ADS  Google Scholar 

  41. L.B. Castro and L.A. Meza, Fermion localization on branes with generalized dynamics, arXiv:1011.5872 [SPIRES].

  42. A.E.R. Chumbes, A.E.O. Vasquez and M.B. Hott, Fermion localization on a split brane, Phys. Rev. D 83 (2011) 105010 [arXiv:1012.1480] [SPIRES].

    ADS  Google Scholar 

  43. L.B. Castro and L.A. Meza, Effect of the variation of mass on fermion localization on thick branes, arXiv:1104.5402 [SPIRES].

  44. C.A.S. Almeida, M.M. Ferreira, Jr., A.R. Gomes and R. Casana, Fermion localization and resonances on two-field thick branes, Phys. Rev. D 79 (2009) 125022 [arXiv:0901.3543] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  45. W.T. Cruz, M.O. Tahim and C.A.S. Almeida, Gauge field localization on a dilatonic deformed brane, Phys. Lett. B 686 (2010) 259 [SPIRES].

    ADS  Google Scholar 

  46. W.T. Cruz, M.O. Tahim and C.A.S. Almeida, Results in Kalb-Ramond field localization and resonances on deformed branes, Europhys. Lett. 88 (2009) 41001 [arXiv:0912.1029] [SPIRES].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil

    R. R. Landim & R. N. Costa Filho

  2. Universidade Estadual do Ceará Faculdade de Educação, Ciências e Letras do Sertão Central-R. Epitcio Pessoa, 2554, 63.900-000 Quixadá, Ceará, Brazil

    G. Alencar & M. O. Tahim

Authors
  1. R. R. Landim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Alencar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. O. Tahim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. N. Costa Filho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Alencar.

Additional information

This paper is dedicated to the memory of my wife Isabel Mara (R. R. Landim)

ArXiv ePrint: 1105.5573

Rights and permissions

Reprints and permissions

About this article

Cite this article

Landim, R.R., Alencar, G., Tahim, M.O. et al. A transfer matrix method for resonances in Randall-Sundrum models. J. High Energ. Phys. 2011, 71 (2011). https://doi.org/10.1007/JHEP08(2011)071

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP08(2011)071

Keywords

Search

Navigation