Abstract
We review the relation between four-dimensional global conformal blocks and field propagation in AdS5. Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar fields in the generic Kerr-AdS5 geometry. On one hand, the result for scattering coefficients can be obtained exactly using the isomonodromy technique, giving exact expressions in terms of c = 1 chiral conformal blocks. On the other hand, one can use the analogy between the scalar field equations to the Level 2 null field Ward identity in two dimensional Liouville field theory to write approximate expressions for the same coefficients in terms of semi-classical chiral Liouville conformal blocks. Surprisingly, the conformal block thus constructed has a well-behaved interpretation in terms of Liouville vertex operators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Marolf, Black holes, AdS and CFTs, Gen. Rel. Grav. 41 (2009) 903 [arXiv:0810.4886] [INSPIRE].
L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, Novel local CFT and exact results on perturbations of N = 4 super Yang-Mills from AdS dynamics, JHEP 12 (1998) 022 [hep-th/9810126] [INSPIRE].
O. DeWolfe, D.Z. Freedman, S.S. Gubser and A. Karch, Modeling the fifth-dimension with scalars and gravity, Phys. Rev. D 62 (2000) 046008 [hep-th/9909134] [INSPIRE].
E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].
G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
S. Jackson, L. McGough and H. Verlinde, Conformal bootstrap, universality and gravitational scattering, Nucl. Phys. B 901 (2015) 382 [arXiv:1412.5205] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
A. Neitzke, Greybody factors at large imaginary frequencies, hep-th/0304080 [INSPIRE].
L. Motl and A. Neitzke, Asymptotic black hole quasinormal frequencies, Adv. Theor. Math. Phys. 7 (2003) 307 [hep-th/0301173] [INSPIRE].
F. Novaes and B. Carneiro da Cunha, Isomonodromy, Painlevé transcendents and scattering off of black holes, JHEP 07 (2014) 132 [arXiv:1404.5188] [INSPIRE].
B. Carneiro da Cunha and F. Novaes, Kerr-de Sitter greybody factors via isomonodromy, Phys. Rev. D 93 (2016) 024045 [arXiv:1508.04046] [INSPIRE].
O. Gamayun, N. Iorgov and O. Lisovyy, How instanton combinatorics solves Painlevé VI, V and IIIs, J. Phys. A 46 (2013) 335203 [arXiv:1302.1832] [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
V.A. Alba, V.A. Fateev, A.V. Litvinov and G.M. Tarnopolskiy, On combinatorial expansion of the conformal blocks arising from AGT conjecture, Lett. Math. Phys. 98 (2011) 33 [arXiv:1012.1312] [INSPIRE].
I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, Bulk and transhorizon measurements in AdS/CFT, JHEP 10 (2012) 165 [arXiv:1201.3664] [INSPIRE].
A. Castro, J.M. Lapan, A. Maloney and M.J. Rodriguez, Black hole monodromy and conformal field theory, Phys. Rev. D 88 (2013) 044003 [arXiv:1303.0759] [INSPIRE].
A. Castro, J.M. Lapan, A. Maloney and M.J. Rodriguez, Black hole scattering from monodromy, Class. Quant. Grav. 30 (2013) 165005 [arXiv:1304.3781] [INSPIRE].
E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Witten diagrams revisited: the AdS geometry of conformal blocks, JHEP 01 (2016) 146 [arXiv:1508.00501] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Virasoro conformal blocks and thermality from classical background fields, JHEP 11 (2015) 200 [arXiv:1501.05315] [INSPIRE].
B. Carneiro da Cunha and M. Guica, Exploring the BTZ bulk with boundary conformal blocks, arXiv:1604.07383 [INSPIRE].
B. Czech, L. Lamprou, S. McCandlish, B. Mosk and J. Sully, A stereoscopic look into the bulk, JHEP 07 (2016) 129 [arXiv:1604.03110] [INSPIRE].
J. de Boer, F.M. Haehl, M.P. Heller and R.C. Myers, Entanglement, holography and causal diamonds, JHEP 08 (2016) 162 [arXiv:1606.03307] [INSPIRE].
S. Ferrara, A.F. Grillo and R. Gatto, Manifestly conformal covariant operator-product expansion, Lett. Nuovo Cim. 2S2 (1971) 1363 [INSPIRE].
S. Ferrara, A.F. Grillo, G. Parisi and R. Gatto, Canonical scaling and conformal invariance, Phys. Lett. 38B (1972) 333 [INSPIRE].
S. Ferrara, A.F. Grillo, G. Parisi and R. Gatto, Covariant expansion of the conformal four-point function, Nucl. Phys. B 49 (1972) 77 [Erratum ibid. B 53 (1973) 643] [INSPIRE].
A. Castro, A. Maloney and A. Strominger, Hidden conformal symmetry of the Kerr black hole, Phys. Rev. D 82 (2010) 024008 [arXiv:1004.0996] [INSPIRE].
D. Simmons-Duffin, Projectors, shadows and conformal blocks, JHEP 04 (2014) 146 [arXiv:1204.3894] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, E. Katz and L. Randall, Decoupling of high dimension operators from the low energy sector in holographic models, arXiv:1304.3458 [INSPIRE].
M. Bochicchio, An asymptotic solution of large-N QCD and of large-N \( \mathcal{N}=1 \) SUSY YM, arXiv:1409.5149 [INSPIRE].
S.W. Hawking, C.J. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [INSPIRE].
H. Lü, J. Mei and C.N. Pope, Kerr/CFT correspondence in diverse dimensions, JHEP 04 (2009) 054 [arXiv:0811.2225] [INSPIRE].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
G.W. Gibbons, M.J. Perry and C.N. Pope, The first law of thermodynamics for Kerr-anti-de Sitter black holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [INSPIRE].
H.K. Kunduri and J. Lucietti, Integrability and the Kerr-(A)dS black hole in five dimensions, Phys. Rev. D 71 (2005) 104021 [hep-th/0502124] [INSPIRE].
A.N. Aliev and O. Delice, Superradiant instability of five-dimensional rotating charged AdS black holes, Phys. Rev. D 79 (2009) 024013 [arXiv:0808.0280] [INSPIRE].
K. Iwasaki, H. Kimura, S. Shimomura and M. Yoshida, From Gauss to Painlevé: a modern theory of special functions, Aspects of Mathematics E volume 16, Braunschweig, Germany (1991).
M. Jimbo, Monodromy problem and the boundary condition for some Painlevé equations, Publ. Res. Inst. Math. Sci. 18 (1982) 1137.
O. Gamayun, N. Iorgov and O. Lisovyy, Conformal field theory of Painlevé VI, JHEP 10 (2012) 038 [Erratum ibid. 10 (2012) 183] [arXiv:1207.0787] [INSPIRE].
A. Litvinov, S. Lukyanov, N. Nekrasov and A. Zamolodchikov, Classical conformal blocks and Painlevè VI, JHEP 07 (2014) 144 [arXiv:1309.4700] [INSPIRE].
N. Iorgov, O. Lisovyy and J. Teschner, Isomonodromic τ -functions from Liouville conformal blocks, Commun. Math. Phys. 336 (2015) 671 [arXiv:1401.6104] [INSPIRE].
D. Harlow, J. Maltz and E. Witten, Analytic continuation of Liouville theory, JHEP 12 (2011) 071 [arXiv:1108.4417] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Sénéchal, Conformal field theory, Springer, Germany (1997).
A.B. Zamolodchikov, Two-dimensional conformal symmetry and critical four-spin correlation functions in the Ashkin-Teller model, Zh. Eksp. Teor. Fiz. 90 (1986) 1808.
S. Winitzki, Cosmological particle production and the precision of the WKB approximation, Phys. Rev. D 72 (2005) 104011 [gr-qc/0510001] [INSPIRE].
G. Siopsis, On quasi-normal modes and the AdS 5 /CF T 4 correspondence, Nucl. Phys. B 715 (2005) 483 [hep-th/0407157] [INSPIRE].
M. Bochicchio, Renormalization in large-N QCD is incompatible with open/closed string duality, arXiv:1703.10176 [INSPIRE].
M. Bochicchio, Asymptotic freedom versus open/closed duality in large-N QCD, Phys. Rev. D 95 (2017) 054010 [arXiv:1606.04546] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1702.01016
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Amado, J.B., da Cunha, B.C. & Pallante, E. On the Kerr-AdS/CFT correspondence. J. High Energ. Phys. 2017, 94 (2017). https://doi.org/10.1007/JHEP08(2017)094
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2017)094