×

zbMATH — the first resource for mathematics

On quasi-normal modes and the \(\text{AdS}_5/\text{CFT}_4\) correspondence. (English) Zbl 1207.81137
Summary: We discuss the quasi-normal modes of massive scalar perturbations of black holes in \(\text{AdS}_5\) in conjunction with the AdS/CFT correspondence. On the gravity side, we solve the wave equation and obtain an expression for the asymptotic form of quasi-normal frequencies. We then show that these expressions agree with those obtained from a CFT defined on \(\mathbb R\times S^3\) in a certain scaling limit, by identifying Euclidean time with one of the periodic coordinates. This generalizes known exact results in three dimensions (BTZ black hole). As a by-product, we derive the standard energy quantization condition in AdS by a simple monodromy argument in complexified AdS space. This argument relies on an unphysical singularity.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Chan, J.S.F.; Mann, R.B., Phys. rev. D, 55, 7546, (1997)
[2] Horowitz, G.T.; Hubeny, V.E., Phys. rev. D, 62, 024027, (2000)
[3] Horowitz, G.T., Class. quantum grav., 17, 1107, (2000)
[4] Wang, B.; Lin, C.Y.; Abdalla, E., Phys. lett. B, 481, 79, (2000)
[5] Wang, B.; Molina, C.; Abdalla, E.
[6] Govindarajan, T.R.; Suneeta, V., Class. quantum grav., 18, 265, (2001)
[7] Cardoso, V.; Lemos, J.P.S., Phys. rev. D, 63, 124015, (2001)
[8] Cardoso, V.; Lemos, J.P.S., Phys. rev. D, 64, 084017, (2001)
[9] Cardoso, V.; Lemos, J.P.S., Class. quantum grav., 18, 5257, (2001)
[10] Zhu, J.M.; Wang, B.; Abdalla, E., Phys. rev. D, 63, 124004, (2001)
[11] Wang, B.; Abdalla, E.; Mann, R.B., Phys. rev. D, 65, 084006, (2002)
[12] Birmingham, D., Phys. rev. D, 64, 064024, (2001)
[13] Birmingham, D.; Sachs, I.; Solodukhin, S.N., Phys. rev. lett., 88, 151301, (2002)
[14] Kurita, Y.; Sakagami, M., Phys. rev. D, 67, 024003, (2003)
[15] Son, D.T.; Starinets, A.O., Jhep, 0209, 042, (2002)
[16] Aros, R.; Martinez, C.; Troncoso, R.; Zanelli, J., Phys. rev. D, 67, 044014, (2003)
[17] Cardoso, V.; Dias, O.J.C.; Lemos, J.P.S., Phys. rev. D, 67, 064026, (2003)
[18] Cardoso, V.; Konoplya, R.; Lemos, J.P.S., Phys. rev. D, 68, (2003)
[19] Cardoso, V.; Natario, J.; Schiappa, R.
[20] Starinets, A.O., Phys. rev. D, 66, 124013, (2002)
[21] Konoplya, R.A., Phys. rev. D, 66, 044009, (2002)
[22] Konoplya, R.A., Phys. rev. D, 66, 084007, (2002)
[23] Slavyanov, S.Y.; Lay, W., Special functions: A unified theory based on singularities, (), (2000), Oxford Univ. Press Oxford · Zbl 1064.33006
[24] Musiri, S.; Siopsis, G., Phys. lett. B, 563, 102, (2003)
[25] Musiri, S.; Siopsis, G., Phys. lett. B, 576, 309, (2003)
[26] Siopsis, G., Phys. lett. B, 590, 105, (2004)
[27] Núñez, A.; Starinets, A.O., Phys. rev. D, 67, 124013, (2003)
[28] Fidkowski, L.; Hubeny, V.; Kleban, M.; Shenker, S., Jhep, 0402, 014, (2004)
[29] Balasubramanian, V.; Levi, T.S.
[30] Krasnov, K.; Solodukhin, S.N., Adv. theor. math. phys., 8, 421, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.