Abstract
Extremal black branes upon compactification in the near horizon throat region are known to give rise to AdS2 dilaton-gravity-matter theories. Away from the throat region, the background has nontrivial profile. We interpret this as holographic renormalization group flow in the 2-dim dilaton-gravity-matter theories arising from dimensional reduction of the higher dimensional theories here. The null energy conditions allow us to formulate a holographic c-function in terms of the 2-dim dilaton for which we argue a c-theorem subject to appropriate boundary conditions which amount to restrictions on the ultraviolet theories containing these extremal branes. At the infrared AdS2 fixed point, the c-function becomes the extremal black brane entropy. We discuss the behaviour of this inherited c-function in various explicit examples, in particular compactified nonconformal branes, and compare it with other discussions of holographic c-functions. We also adapt the holographic renormalization group formulated in terms of radial Hamiltonian flow to 2-dim dilaton-gravity-scalar theories, which while not Wilsonian, gives qualitative insight into the flow equations and β-functions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
K. Jensen, Chaos in AdS 2 holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
A. Almheiri and B. Kang, Conformal symmetry breaking and thermodynamics of near-extremal black holes, JHEP 10 (2016) 052 [arXiv:1606.04108] [INSPIRE].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999)011 [hep-th/9812073] [INSPIRE].
A. Sen, Quantum entropy function from AdS 2 /CFT 1 correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, A simple model of quantum holography (part 1), talk at the KITP, http://online.kitp.ucsb.edu/online/entangled15/kitaev/, University of California, Santa Barbara, CA, U.S.A. 7 April 2015.
A. Kitaev, A simple model of quantum holography (part 2), talk at the KITP, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/, University of California, Santa Barbara, CA, U.S.A. 27 May 2015.
J. Polchinski and V. Rosenhaus, The spectrum in the Sachdev-Ye-Kitaev model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
G. Sárosi, AdS 2 holography and the SYK model, PoS(Modave2017)001 (2018) [arXiv:1711.08482] [INSPIRE].
V. Rosenhaus, An introduction to the SYK model, arXiv:1807.03334 [INSPIRE].
E.T. Akhmedov, A remark on the AdS/CFT correspondence and the renormalization group flow, Phys. Lett. B 442 (1998) 152 [hep-th/9806217] [INSPIRE].
E. Alvarez and C. Gomez, Geometric holography, the renormalization group and the c theorem, Nucl. Phys. B 541 (1999) 441 [hep-th/9807226] [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].
J. Distler and F. Zamora, Nonsupersymmetric conformal field theories from stable anti-de Sitter spaces, Adv. Theor. Math. Phys. 2 (1999) 1405 [hep-th/9810206] [INSPIRE].
V. Balasubramanian and P. Kraus, Space-time and the holographic renormalization group, Phys. Rev. Lett. 83 (1999) 3605 [hep-th/9903190] [INSPIRE].
K. Skenderis and P.K. Townsend, Gravitational stability and renormalization group flow, Phys. Lett. B 468 (1999) 46 [hep-th/9909070] [INSPIRE].
L. Susskind and E. Witten, The holographic bound in anti-de Sitter space, hep-th/9805114 [INSPIRE].
A.W. Peet and J. Polchinski, UV/IR relations in AdS dynamics, Phys. Rev. D 59 (1999) 065011 [hep-th/9809022] [INSPIRE].
J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [INSPIRE].
E.P. Verlinde and H.L. Verlinde, RG flow, gravity and the cosmological constant, JHEP 05 (2000)034 [hep-th/9912018] [INSPIRE].
J. de Boer, The holographic renormalization group, Fortsch. Phys. 49 (2001) 339 [hep-th/0101026] [INSPIRE].
A.B. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett. 43 (1986) 730 [Pisma Zh. Eksp. Teor. Fiz. 43 (1986) 565] [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].
R. Bousso, A covariant entropy conjecture, JHEP 07 (1999) 004 [hep-th/9905177] [INSPIRE].
V. Sahakian, Holography, a covariant c function and the geometry of the renormalization group, Phys. Rev. D 62 (2000) 126011 [hep-th/9910099] [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].
I. Heemskerk and J. Polchinski, Holographic and Wilsonian renormalization groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].
T. Faulkner, H. Liu and M. Rangamani, Integrating out geometry: holographic Wilsonian RG and the membrane paradigm, JHEP 08 (2011) 051 [arXiv:1010.4036] [INSPIRE].
T. Nishioka, Entanglement entropy: holography and renormalization group, Rev. Mod. Phys. 90 (2018) 035007 [arXiv:1801.10352] [INSPIRE].
K.S. Kolekar and K. Narayan, AdS 2 dilaton gravity from reductions of some nonrelativistic theories, Phys. Rev. D 98 (2018) 046012 [arXiv:1803.06827] [INSPIRE].
A. Castro and W. Song, Comments on AdS 2 gravity, arXiv:1411.1948 [INSPIRE].
M. Cvetič and I. Papadimitriou, AdS 2 holographic dictionary, JHEP 12 (2016) 008 [Erratum ibid. 01 (2017) 120] [arXiv:1608.07018] [INSPIRE].
S.R. Das, A. Jevicki and K. Suzuki, Three dimensional view of the SYK/AdS duality, JHEP 09 (2017) 017 [arXiv:1704.07208] [INSPIRE].
M. Taylor, Generalized conformal structure, dilaton gravity and SYK, JHEP 01 (2018) 010 [arXiv:1706.07812] [INSPIRE].
A. Gaikwad, L.K. Joshi, G. Mandal and S.R. Wadia, Holographic dual to charged SYK from 3D gravity and Chern-Simons, arXiv:1802.07746 [INSPIRE].
P. Nayak, A. Shukla, R.M. Soni, S.P. Trivedi and V. Vishal, On the dynamics of near-extremal black holes, JHEP 09 (2018) 048 [arXiv:1802.09547] [INSPIRE].
U. Moitra, S.P. Trivedi and V. Vishal, Near-extremal near-horizons, arXiv:1808.08239 [INSPIRE].
M. Cadoni, M. Ciulu and M. Tuveri, Symmetries, holography and quantum phase transition in two-dimensional dilaton AdS gravity, Phys. Rev. D 97 (2018) 103527 [arXiv:1711.02459] [INSPIRE].
Y.-Z. Li, S.-L. Li and H. Lü, Exact embeddings of JT gravity in strings and M-theory, Eur. Phys. J. C 78 (2018) 791 [arXiv:1804.09742] [INSPIRE].
A. Castro, F. Larsen and I. Papadimitriou, 5D rotating black holes and the nAdS 2 /nCFT 1 correspondence, JHEP 10 (2018) 042 [arXiv:1807.06988] [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].
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
J. Tarrio and S. Vandoren, Black holes and black branes in Lifshitz spacetimes, JHEP 09 (2011) 017 [arXiv:1105.6335] [INSPIRE].
M. Alishahiha, E. O Colgain and H. Yavartanoo, Charged black branes with hyperscaling violating factor, JHEP 11 (2012) 137 [arXiv:1209.3946] [INSPIRE].
P. Bueno, W. Chemissany, P. Meessen, T. Ortín and C.S. Shahbazi, Lifshitz-like solutions with hyperscaling violation in ungauged supergravity, JHEP 01 (2013) 189 [arXiv:1209.4047] [INSPIRE].
R. Jackiw, Lower dimensional gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
J.T. Liu and Z. Zhao, Holographic Lifshitz flows and the null energy condition, arXiv:1206.1047 [INSPIRE].
J.T. Liu and W. Zhong, A holographic c-theorem for Schrödinger spacetimes, JHEP 12 (2015)179 [arXiv:1510.06975] [INSPIRE].
X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
J.L.F. Barbon and C.A. Fuertes, Holographic entanglement entropy probes (non)locality, JHEP 04 (2008) 096 [arXiv:0803.1928] [INSPIRE].
K. Narayan, Non-conformal brane plane waves and entanglement entropy, Phys. Lett. B 726 (2013) 370 [arXiv:1304.6697] [INSPIRE].
D. Mukherjee and K. Narayan, AdS plane waves, entanglement and mutual information, Phys. Rev. D 90 (2014) 026003 [arXiv:1405.3553] [INSPIRE].
J.P. Gauntlett and O. Varela, Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions, Phys. Rev. D 76 (2007) 126007 [arXiv:0707.2315] [INSPIRE].
H. Casini and M. Huerta, A c-theorem for the entanglement entropy, J. Phys. A 40 (2007) 7031 [cond-mat/0610375] [INSPIRE].
H. Casini and M. Huerta, On the RG running of the entanglement entropy of a circle, Phys. Rev. D 85 (2012) 125016 [arXiv:1202.5650] [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].
R.C. Myers and A. Singh, Comments on holographic entanglement entropy and RG flows, JHEP 04 (2012) 122 [arXiv:1202.2068] [INSPIRE].
S. Cremonini and X. Dong, Constraints on renormalization group flows from holographic entanglement entropy, Phys. Rev. D 89 (2014) 065041 [arXiv:1311.3307] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
V. Sahakian, Comments on D-branes and the renormalization group, JHEP 05 (2000) 011 [hep-th/0002126] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [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].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].
D. Anninos and D.M. Hofman, Infrared realization of dS 2 in AdS 2, Class. Quant. Grav. 35 (2018) 085003 [arXiv:1703.04622] [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: 1810.12528
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
Kolekar, K.S., Narayan, K. On AdS2 holography from redux, renormalization group flows and c-functions. J. High Energ. Phys. 2019, 39 (2019). https://doi.org/10.1007/JHEP02(2019)039
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2019)039