Abstract
Using the attractor mechanism for extremal solutions in \( \mathcal{N}=2 \) gauged supergravity, we construct a c-function that interpolates between the central charges of theories at ultraviolet and infrared conformal fixed points corresponding to anti-de Sitter geometries. The c-function we obtain is couched purely in terms of bulk quantities and connects two different dimensional CFTs at the stable conformal fixed points under the RG flow.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
A.B. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett. 43 (1986) 730 [INSPIRE].
J.L. Cardy, Is there a c theorem in four-dimensions?, Phys. Lett. B 215 (1988) 749 [INSPIRE].
H. Osborn, Derivation of a four-dimensional c theorem, Phys. Lett. B 222 (1989) 97 [INSPIRE].
I. Jack and H. Osborn, Analogs for the c theorem for four-dimensional renormalizable field theories, Nucl. Phys. B 343 (1990) 647 [INSPIRE].
Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
Z. Komargodski, The constraints of conformal symmetry on RG flows, JHEP 07 (2012) 069 [arXiv:1112.4538] [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].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [INSPIRE].
G. Lopes Cardoso, G. Dall’Agata and D. Lüst, Curved BPS domain walls and RG flow in five-dimensions, JHEP 03 (2002) 044 [hep-th/0201270] [INSPIRE].
R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [arXiv:1006.1263] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
J.T. Liu, W. Sabra and Z. Zhao, Holographic c-theorems and higher derivative gravity, Phys. Rev. D 85 (2012) 126004 [arXiv:1012.3382] [INSPIRE].
M.F. Paulos, Holographic phase space: c-functions and black holes as renormalization group flows, JHEP 05 (2011) 043 [arXiv:1101.5993] [INSPIRE].
K. Goldstein, R.P. Jena, G. Mandal and S.P. Trivedi, A c-function for non-supersymmetric attractors, JHEP 02 (2006) 053 [hep-th/0512138] [INSPIRE].
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072] [INSPIRE].
A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B 383 (1996) 39 [hep-th/9602111] [INSPIRE].
S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev. D 54 (1996) 1514 [hep-th/9602136] [INSPIRE].
S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525 [hep-th/9603090] [INSPIRE].
A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [INSPIRE].
K. Goldstein, N. Iizuka, R.P. Jena and S.P. Trivedi, Non-supersymmetric attractors, Phys. Rev. D 72 (2005) 124021 [hep-th/0507096] [INSPIRE].
D. Astefanesei, K. Goldstein, R.P. Jena, A. Sen and S.P. Trivedi, Rotating attractors, JHEP 10 (2006) 058 [hep-th/0606244] [INSPIRE].
A. Dabholkar, A. Sen and S.P. Trivedi, Black hole microstates and attractor without supersymmetry, JHEP 01 (2007) 096 [hep-th/0611143] [INSPIRE].
A. Sen, Black hole entropy function, attractors and precision counting of microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
K. Skenderis and P.K. Townsend, Gravitational stability and renormalization group flow, Phys. Lett. B 468 (1999) 46 [hep-th/9909070] [INSPIRE].
J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
V. Balasubramanian, J. de Boer, M.M. Sheikh-Jabbari and J. Simon, What is a chiral 2D CFT? And what does it have to do with extremal black holes?, JHEP 02 (2010) 017 [arXiv:0906.3272] [INSPIRE].
E. D’Hoker and P. Kraus, Magnetic brane solutions in AdS, JHEP 10 (2009) 088 [arXiv:0908.3875] [INSPIRE].
A. Almuhairi, AdS 3 and AdS 2 magnetic brane solutions, arXiv:1011.1266 [INSPIRE].
A. Almuhairi and J. Polchinski, Magnetic AdS × R 2 : supersymmetry and stability, arXiv:1108.1213 [INSPIRE].
A. Almheiri, Magnetic AdS 2 × R 2 at weak and strong coupling, arXiv:1112.4820 [INSPIRE].
S. Jain, N. Kundu, K. Sen, A. Sinha and S.P. Trivedi, A strongly coupled anisotropic fluid from dilaton driven holography, arXiv:1406.4874 [INSPIRE].
S. Barisch-Dick, G. Lopes Cardoso, M. Haack and S. Nampuri, Extremal black brane solutions in five-dimensional gauged supergravity, JHEP 02 (2013) 103 [arXiv:1211.0832] [INSPIRE].
G. Dall’Agata and A. Gnecchi, Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity, JHEP 03 (2011) 037 [arXiv:1012.3756] [INSPIRE].
S. Barisch, G. Lopes Cardoso, M. Haack, S. Nampuri and N.A. Obers, Nernst branes in gauged supergravity, JHEP 11 (2011) 090 [arXiv:1108.0296] [INSPIRE].
S. Barisch-Dick, G.L. Cardoso, M. Haack and Á. Véliz-Osorio, Quantum corrections to extremal black brane solutions, JHEP 02 (2014) 105 [arXiv:1311.3136] [INSPIRE].
K. Hristov and A. Rota, Attractors, black objects and holographic RG flows in 5D maximal gauged supergravities, JHEP 03 (2014) 057 [arXiv:1312.3275] [INSPIRE].
I.R. Klebanov, S.S. Pufu and B.R. Safdi, F-theorem without supersymmetry, JHEP 10 (2011) 038 [arXiv:1105.4598] [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-theorem: N = 2 field theories on the three-sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
A. Sen, State operator correspondence and entanglement in AdS 2 /CFT 1, Entropy 13 (2011) 1305 [arXiv:1101.4254] [INSPIRE].
J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
T. Banks and E.J. Martinec, The renormalization group and string field theory, Nucl. Phys. B 294 (1987) 733 [INSPIRE].
J. Hughes, J. Liu and J. Polchinski, Virasoro-shapiro from Wilson, Nucl. Phys. B 316 (1989) 15 [INSPIRE].
V. Balasubramanian, E.G. Gimon, D. Minic and J. Rahmfeld, Four-dimensional conformal supergravity from AdS space, Phys. Rev. D 63 (2001) 104009 [hep-th/0007211] [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
A. Donos and J.P. Gauntlett, Lifshitz solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [INSPIRE].
J. de Boer, J. Manschot, K. Papadodimas and E. Verlinde, The chiral ring of AdS 3 /CFT 2 and the attractor mechanism, JHEP 03 (2009) 030 [arXiv:0809.0507] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Spacetime geometry in higher spin gravity, JHEP 10 (2011) 053 [arXiv:1106.4788] [INSPIRE].
M.M. Anber and D. Kastor, The attractor mechanism in Gauss-Bonnet gravity, JHEP 10 (2007) 084 [arXiv:0707.1464] [INSPIRE].
M.M. Anber and D. Kastor, C-functions in Lovelock gravity, JHEP 05 (2008) 061 [arXiv:0802.1290] [INSPIRE].
M.R. Garousi and A. Ghodsi, On attractor mechanism and entropy function for non-extremal black holes/branes, JHEP 05 (2007) 043 [hep-th/0703260] [INSPIRE].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, 5D attractors with higher derivatives, JHEP 04 (2007) 091 [hep-th/0702072] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1407.0469
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Bhattacharyya, A., Haque, S.S., Jejjala, V. et al. Attractive holographic c-functions. J. High Energ. Phys. 2014, 138 (2014). https://doi.org/10.1007/JHEP11(2014)138
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2014)138