The vacuum expectation value of the surface energy-momentum tensor of a charged scalar field on a flat brane in an anti-de Sitter space-time with a compact spatial dimension is studied. The existence of a constant gauge field is also assumed. Because of the nontrivial topology of the space, the latter leads to an Aharonov-Bohm type effect. A generalized zeta-function method is used for renormalizing the vacuum expectation value. The cosmological constant induced on the brane is a periodic function of the magnetic flux through the compact dimension and, depending on the parameters of the problem, can be either positive or negative.
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References
R. Maartens and K. Koyama, Living Rev. Relativity 13, 5 (2010).
V. M. Mostepanenko and N. N. Trunov, The Casimir Effect and its Applications, Clarendon, Oxford (1997).
K. A. Milton, The Casimir Effect: Physical Manifestation of Zero-Point Energy, World Scientific, Singapore (2002).
M. Bordag, G. L. Klimchitskaya, U. Mohideen, et al., Advances in the Casimir Effect, Oxford University Press, Oxford (2009).
D. Dalvit, P. Milonni, D. Roberts, and F. da Rosa, ed., Casimir Physics, Lecture Notes in Physics 834, Springer-Verlag, Berlin (2011).
E. R. Bezerra de Mello, A. A. Saharian, and M. R. Setare, Phys. Rev. D 92, 104005 (2015).
A. A. Saharian and M. R. Setare, Phys. Lett. B 552, 119 (2003).
A. Knapman and D. J. Toms, Phys. Rev. D 69, 044023 (2004).
A. A. Saharian, Nucl. Phys. B 712, 196 (2005).
A. A. Saharian, Phys. Rev. D 73, 044012 (2006).
A. A. Saharian, Phys. Rev. D 73, 064019 (2006).
S.-H. Shao, P. Chen, and J.-A. Gu, Phys. Rev. D 81, 084036 (2010).
E. Elizalde, S. D. Odintsov, and A. A. Saharian, Phys. Rev. D 87, 084003 (2013).
A. A. Saharian, A. S. Kotanjyan, and A. A. Saharyan, Proc. Yerevan State Univ., Phys. and Math. Sci. 3, 37 (2016).
A. S. Kotanjyan, A. A. Saharian, and A. A. Saharyan, Galaxies 5, 102 (2017).
A. A. Saharian, Phys. Rev. D 69, 085005 (2004).
A. A. Saharian, Phys. Rev. D 70, 064026 (2004).
A. A. Saharian, Phys. Rev. D 74, 124009 (2006).
E. R. Bezerra de Mello, A. A. Saharian, and V. Vardanyan, Phys. Lett. B 741, 155 (2015).
S. Bellucci, A. A. Saharian, and V. Vardanyan, J. High Energy Phys. 11, 092 (2015).
S. Bellucci, A. A. Saharian, and V. Vardanyan, Phys. Rev. D 93, 084011 (2016).
E. Elizalde, S. D. Odintsov, A. Romeo, et al., Zeta Regularization Techniques with Applications, World Scientific, Singapore (1994).
B. Greene and J. Levin, J. High Energy Phys. 11, 096 (2007).
A. O. Barvinskii, Usp. Fiz. Nauk 175, 569 (2005).
B. P. Abbott, et al., Phys. Rev. Lett. 119, 161101 (2017).
L. Visinelli, N. Bolis, S. Vagnozzi, Phys. Rev. D 97, 064039 (2018).
M. D. Douglas, Sh. Kachru, Rev. Mod. Phys. 79, 733 (2007).
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Translated from Astrofizika, Vol. 61, No. 3, pp. 423-437 (August 2018).
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Saharian, A.A., Sargsyan, H.G. Induced Cosmological Constant in Brane Models with a Compact Dimension. Astrophysics 61, 375–390 (2018). https://doi.org/10.1007/s10511-018-9544-7
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DOI: https://doi.org/10.1007/s10511-018-9544-7