Abstract
We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entan-glement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduc-tion over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.
Article PDF
Similar content being viewed by others
References
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
A. Lewkowycz and J.M. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
T. Takayanagi, Entanglement Entropy from a Holographic Viewpoint, Class. Quant. Grav. 29 (2012) 153001 [arXiv:1204.2450] [INSPIRE].
M. Headrick, General properties of holographic entanglement entropy, JHEP 03 (2014) 085 [arXiv:1312.6717] [INSPIRE].
I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
T. Nishioka and T. Takayanagi, AdS Bubbles, Entropy and Closed String Tachyons, JHEP 01 (2007) 090 [hep-th/0611035] [INSPIRE].
I. Bah, A. Faraggi, L.A. Pando Zayas and C.A. Terrero-Escalante, Holographic entanglement entropy and phase transitions at finite temperature, Int. J. Mod. Phys. A 24 (2009) 2703 [arXiv:0710.5483] [INSPIRE].
D. Arean, P. Merlatti, C. Núñez and A.V. Ramallo, String duals of two-dimensional (4,4) supersymmetric gauge theories, JHEP 12 (2008) 054 [arXiv:0810.1053] [INSPIRE].
A.V. Ramallo, J.P. Shock and D. Zoakos, Holographic flavor in N = 4 gauge theories in 3d from wrapped branes, JHEP 02 (2009) 001 [arXiv:0812.1975] [INSPIRE].
F. Bigazzi, A.L. Cotrone, A. Paredes and A.V. Ramallo, The Klebanov-Strassler model with massive dynamical flavors, JHEP 03 (2009) 153 [arXiv:0812.3399] [INSPIRE].
S. Bennett, E. Caceres, C. Núñez, D. Schofield and S. Young, The non-SUSY Baryonic Branch: Soft Supersymmetry Breaking of N = 1 Gauge Theories, JHEP 05 (2012) 031 [arXiv:1111.1727] [INSPIRE].
P. Dey and S. Roy, Holographic entanglement entropy of the near horizon 1/4 BPS F-Dp bound states, Phys. Rev. D 87 (2013) 066001 [arXiv:1208.1820] [INSPIRE].
K. Kontoudi and G. Policastro, Flavor corrections to the entanglement entropy, JHEP 01 (2014) 043 [arXiv:1310.4549] [INSPIRE].
Y. Bea, E. Conde, N. Jokela and A.V. Ramallo, Unquenched massive flavors and flows in Chern-Simons matter theories, JHEP 12 (2013) 033 [arXiv:1309.4453] [INSPIRE].
F. Aprile and V. Niarchos, Large-N transitions of the connectivity index, JHEP 02 (2015) 083 [arXiv:1410.7773] [INSPIRE].
K.K. Kim, O.-K. Kwon, C. Park and H. Shin, Renormalized Entanglement Entropy Flow in Mass-deformed ABJM Theory, Phys. Rev. D 90 (2014) 046006 [arXiv:1404.1044] [INSPIRE].
Y. Bea et al., Compactifications of the Klebanov-Witten CFT and new AdS 3 backgrounds, JHEP 05 (2015) 062 [arXiv:1503.07527] [INSPIRE].
S. Giusto, E. Moscato and R. Russo, AdS 3 holography for 1/4 and 1/8 BPS geometries, JHEP 11 (2015) 004 [arXiv:1507.00945] [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].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Continuous distributions of D3-branes and gauged supergravity, JHEP 07 (2000) 038 [hep-th/9906194] [INSPIRE].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].
K. Skenderis and M. Taylor, Kaluza-Klein holography, JHEP 05 (2006) 057 [hep-th/0603016] [INSPIRE].
K. Skenderis and M. Taylor, Holographic Coulomb branch vevs, JHEP 08 (2006) 001 [hep-th/0604169] [INSPIRE].
P.A.R. Jones and M. Taylor, Entanglement entropy and differential entropy for massive flavors, JHEP 08 (2015) 014 [arXiv:1505.07697] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Classification of Gravitational Instanton Symmetries, Commun. Math. Phys. 66 (1979) 291 [INSPIRE].
S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large-N , Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
A. Mollabashi, N. Shiba and T. Takayanagi, Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy, JHEP 04 (2014) 185 [arXiv:1403.1393] [INSPIRE].
M. Taylor, Generalized entanglement entropy, JHEP 07 (2016) 040 [arXiv:1507.06410] [INSPIRE].
J.M. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [INSPIRE].
H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The Mass Spectrum of Chiral N = 2 D = 10 Supergravity on S 5, Phys. Rev. D 32 (1985) 389 [INSPIRE].
F. Bigazzi, A.L. Cotrone, J. Mas, A. Paredes, A.V. Ramallo and J. Tarrio, D3-D7 quark-gluon Plasmas, JHEP 11 (2009) 117 [arXiv:0909.2865] [INSPIRE].
C. Núñez, A. Paredes and A.V. Ramallo, Unquenched Flavor in the Gauge/Gravity Correspondence, Adv. High Energy Phys. 2010 (2010) 196714 [arXiv:1002.1088] [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].
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].
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: 1602.04825
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
Jones, P.A., Taylor, M. Entanglement entropy in top-down models. J. High Energ. Phys. 2016, 158 (2016). https://doi.org/10.1007/JHEP08(2016)158
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2016)158