Skip to main content
SpringerLink
Log in

Electromagnetic quantum effects in anti-de Sitter spacetime

  • Elementary Particles and Fields Theory
  • Published:
Physics of Atomic Nuclei Aims and scope Submit manuscript

Abstract

The two-point functions of the vector potential and of the field tensor for the electromagnetic field in the background of anti-de Sitter (AdS) spacetime are evaluated in an arbitrary number of spatial dimensions. First, we consider the two-point functions in the boundary-free geometry and then generalize the results in the presence of a reflecting boundary parallel to the AdS horizon. By using the expressions for the two-point functions of the field tensor, we investigate the vacuum expectation values of the electric field squared and of the energy–momentum tensor. Simple asymptotic expressions are provided near the AdS boundary and horizon.

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. O. Aharony, S. S. Gubser, J. Maldacena, H. Ooguri, and Y. Oz, Phys. Rep. 323, 183 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  2. V. A. Rubakov, Phys. Usp. 44, 871 (2001)

    Article  ADS  Google Scholar 

  3. P. Brax and C. van de Bruck, Class. Quantum Grav. 20, R201 (2003)

    Article  Google Scholar 

  4. E. Kiritsis, Phys. Rep. 421, 105 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  5. R. Maartens and K. Koyama, Liv. Rev. Relativ. 13, 5 (2010).

    Article  ADS  Google Scholar 

  6. G. Plunien, B. Müller, and W. Greiner, Phys. Rep. 134, 87 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  7. E. Elizalde, S. D. Odintsov, A. Romeo, et al., Zeta Regularization Techniques with Applications (World Scientific, Singapore, 1994)

    Book  MATH  Google Scholar 

  8. V. M. Mostepanenko and N. N. Trunov, The Casimir Effect and Its Applications (Oxford Univ. Press, Oxford, 1997)

    Google Scholar 

  9. K. A. Milton, The Casimir Effect: Physical Manifestation of Zero–Point Energy (World Sci., Singapore, 2001)

    Book  MATH  Google Scholar 

  10. M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Advances in the Casimir Effect (Oxford Univ. Press, Oxford, 2009); Casimir Physics, Ed. by D. Dalvit, P. Milonni, D. Roberts, F. da Rosa, (Springer-Verlag, Berlin, Heidelberg,2011), Lect. Not. Phys., Vol. 834.

    Book  MATH  Google Scholar 

  11. W. D. Goldberger and I. Z. Rothstein, Phys. Lett. B 491, 339 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  12. S. Nojiri, S. D. Odintsov, and S. Zerbini, Class. Quantum Grav. 17, 4855 (2000)

    Article  ADS  Google Scholar 

  13. A. Flachi, I. G. Moss, and D. J. Toms, Phys. Lett. B 518, 153 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  14. I. Brevik, K. A. Milton, S. Nojiri, and S. D. Odintsov, Nucl. Phys. B 599, 305 (2001)

    Article  ADS  Google Scholar 

  15. A. Flachi, I. G. Moss, and D. J. Toms, Phys. Rev. D 64, 105029 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  16. J. Garriga, O. Pujolàs, and T. Tanaka, Nucl. Phys. B 605, 192 (2001)

    Article  ADS  Google Scholar 

  17. A. Flachi and D. J. Toms, Nucl. Phys. B 610, 144 (2001)

    Article  ADS  Google Scholar 

  18. J. Garriga and A. Pomarol, Phys. Lett. B 560, 91 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  19. E. Elizalde, S. Nojiri, S. D. Odintsov, and S. Ogushi, Phys. Rev. D 67, 063515 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  20. A. A. Saharian and M. R. Setare, Phys. Lett. B 584, 306 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  21. A. Flachi, A. Knapman, W. Naylor, and M. Sasaki, Phys. Rev. D 70, 124011 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  22. E. Elizalde, S. Nojiri, and S. D. Odintsov, Phys. Rev. D 70, 043539 (2004)

    Article  ADS  Google Scholar 

  23. E. Elizalde, S. Nojiri, S. D. Odintsov, and P. Wang, Phys. Rev. D71, 103504 (2005)

  24. M. Frank, I. Turan, and L. Ziegler, Phys. Rev. D 76, 015008 (2007)

    Article  ADS  Google Scholar 

  25. L. P. Teo, Phys. Lett. B 682, 259 (2009), H. Cheng, arXiv [hep-th]: 0904.4183 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  26. A. Flachi and T. Tanaka, Phys. Rev. D 80, 124022 (2009)

    Article  ADS  Google Scholar 

  27. M. Rypestøl and I. Brevik, New J. Phys 12, 013022 (2010).

    Article  ADS  Google Scholar 

  28. A. Knapman and D. J. Toms, Phys. Rev. D 69, 044023 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  29. A. A. Saharian, Nucl. Phys. B 712, 196 (2005)

    Article  ADS  Google Scholar 

  30. A. A. Saharian, Phys. Rev. D 70, 064026 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  31. S.-H. Shao, P. Chen, and J.-A. Gu, Phys. Rev. D 81, 084036 (2010)

    Article  ADS  Google Scholar 

  32. E. Elizalde, S. D. Odintsov, and A. A. Saharian, Phys. Rev. D 87, 084003 (2013).

    Article  ADS  Google Scholar 

  33. A. Flachi, J. Garriga, O. Pujolàs, and T. Tanaka, JHEP 0308, 053 (2003)

    Article  ADS  Google Scholar 

  34. A. Flachi and O. Pujolàs, Phys. Rev. D 68, 025023 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  35. A. A. Saharian, Phys. Rev. D 73, 04 4012, 064019 (2006); 74, 124009 (2006)

    Article  MathSciNet  Google Scholar 

  36. E. Elizalde, M. Minamitsuji, and W. Naylor, Phys. Rev. D 75, 064032 (2007)

    Article  ADS  Google Scholar 

  37. R. Linares, H. A. Morales-Técotl, and O. Pedraza, Phys. Rev. D 77, 066012 (2008)

    Article  ADS  Google Scholar 

  38. M. Frank, N. Saad, and I. Turan, Phys. Rev. D 78, 055014 (2008)

    Article  ADS  Google Scholar 

  39. E. Elizalde, S. D. Odintsov, and A. A. Saharian, Phys. Rev. D 79, 065023 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  40. E. R. Bezerra de Mello, A. A. Saharian, and V. Vardanyan, Phys. Lett. B 741, 155 (2015)

    Article  MathSciNet  Google Scholar 

  41. S. Bellucci, A. A. Saharian, and V. Vardanyan, JHEP 1511, 092 (2015).

  42. B. Allen and T. Jacobson, Commun. Math. Phys. 103, 669 (1986).

    Article  ADS  Google Scholar 

  43. A. A Saharian, A. S Kotanjyan, and H. A. Nersisyan, Phys. Lett. B 728, 141 (2014)

    Article  ADS  Google Scholar 

  44. A. S. Kotanjyan, A. A. Saharian, and H. A. Nersisyan, Phys. Scr. 90, 065304 (2015)

    Article  ADS  Google Scholar 

  45. A. S Kotanjyan, A. A Saharian, and H. A. Nersisyan, J. Phys.: Conf. Ser. 496, 012027 (2014).

    Google Scholar 

  46. S. Bellucci and A. A. Saharian, Phys. Rev. D 88, 064034 (2013).

    Article  ADS  Google Scholar 

  47. Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. A. Stegun (Dover, New York, 1972).

  48. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series (Gordon and Breach, New York, 1986), Vol. 2.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Yerevan State University, Yerevan, Armenia

    A. S. Kotanjyan & A. A. Saharian

Authors
  1. A. S. Kotanjyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Saharian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. S. Kotanjyan.

Additional information

The text was submitted by the authors in English.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kotanjyan, A.S., Saharian, A.A. Electromagnetic quantum effects in anti-de Sitter spacetime. Phys. Atom. Nuclei 80, 562–571 (2017). https://doi.org/10.1134/S1063778817030152

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063778817030152

Search

Navigation