Abstract
We give a prescription for calculating the entanglement entropy in holographic probe brane systems by systematically taking the leading order backreaction of the probe brane into account. We find a simple compact double integral formula, which is insensitive to many details of the backreaction, most notably the internal space or the non-metric fields sourced by the probe. We validate our method by comparing to exact results in solvable toy models. We also determine the entanglement entropies for a sphere and a strip in the top-down D3/D7 and D3/D5 system. For the sphere the entanglement entropy has also been obtained by other methods and we find perfect agreement.
Article PDF
Similar content being viewed by others
References
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
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].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
T. Takayanagi, Entanglement entropy from a holographic viewpoint, Class. Quant. Grav. 29 (2012) 153001 [arXiv:1204.2450] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
A. Karch and L. Randall, Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].
S. Kachru, A. Karch and S. Yaida, Holographic lattices, dimers and glasses, Phys. Rev. D 81 (2010) 026007 [arXiv:0909.2639] [INSPIRE].
K. Jensen, S. Kachru, A. Karch, J. Polchinski and E. Silverstein, Towards a holographic marginal Fermi liquid, Phys. Rev. D 84 (2011) 126002 [arXiv:1105.1772] [INSPIRE].
K. Jensen, A. Karch, D.T. Son and E.G. Thompson, Holographic Berezinskii-Kosterlitz-Thouless transitions, Phys. Rev. Lett. 105 (2010) 041601 [arXiv:1002.3159] [INSPIRE].
A. Karch, D. Son and A. Starinets, Zero sound from holography, arXiv:0806.3796 [INSPIRE].
M. Kulaxizi and A. Parnachev, Holographic responses of fermion matter, Nucl. Phys. B 815 (2009) 125 [arXiv:0811.2262] [INSPIRE].
A. Karch, M. Kulaxizi and A. Parnachev, Notes on properties of holographic matter, JHEP 11 (2009) 017 [arXiv:0908.3493] [INSPIRE].
H.-C. Chang and A. Karch, Novel solutions of finite-density D3/D5 probe brane system and their implications for stability, JHEP 10 (2012) 069 [arXiv:1207.7078] [INSPIRE].
M. Ammon, K. Jensen, K.-Y. Kim, J.N. Laia and A. O’Bannon, Moduli spaces of cold holographic matter, JHEP 11 (2012) 055 [arXiv:1208.3197] [INSPIRE].
M. Ammon, M. Kaminski and A. Karch, Hyperscaling-violation on probe D-branes, JHEP 11 (2012) 028 [arXiv:1207.1726] [INSPIRE].
N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi surfaces and entanglement entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [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].
M. Fujita, W. Li, S. Ryu and T. Takayanagi, Fractional quantum hall effect via holography: Chern-Simons, edge states and hierarchy, JHEP 06 (2009) 066 [arXiv:0901.0924] [INSPIRE].
C. Hoyos-Badajoz, K. Jensen and A. Karch, A holographic fractional topological insulator, Phys. Rev. D 82 (2010) 086001 [arXiv:1007.3253] [INSPIRE].
T. Azeyanagi, A. Karch, T. Takayanagi and E.G. Thompson, Holographic calculation of boundary entropy, JHEP 03 (2008) 054 [arXiv:0712.1850] [INSPIRE].
M. Chiodaroli, M. Gutperle and L.-Y. Hung, Boundary entropy of supersymmetric Janus solutions, JHEP 09 (2010) 082 [arXiv:1005.4433] [INSPIRE].
E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton and gauge boson propagators in AdS(d + 1), Nucl. Phys. B 562 (1999) 330 [hep-th/9902042] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
M. Nozaki, T. Numasawa, A. Prudenziati and T. Takayanagi, Dynamics of entanglement entropy from Einstein equation, Phys. Rev. D 88 (2013) 026012 [arXiv:1304.7100] [INSPIRE].
G. Wong, I. Klich, L.A. Pando Zayas and D. Vaman, Entanglement temperature and entanglement entropy of excited states, JHEP 12 (2013) 020 [arXiv:1305.3291] [INSPIRE].
Y. Hikida, W. Li and T. Takayanagi, ABJM with flavors and FQHE, JHEP 07 (2009) 065 [arXiv:0903.2194] [INSPIRE].
D. Gaiotto and D.L. Jafferis, Notes on adding D6 branes wrapping Rp 3 in AdS 4 × CP 3, JHEP 11 (2012) 015 [arXiv:0903.2175] [INSPIRE].
S. Hohenegger and I. Kirsch, A note on the holography of Chern-Simons matter theories with flavour, JHEP 04 (2009) 129 [arXiv:0903.1730] [INSPIRE].
M. Ammon, J. Erdmenger, R. Meyer, A. O’Bannon and T. Wrase, Adding flavor to AdS 4 /CFT 3, JHEP 11 (2009) 125 [arXiv:0909.3845] [INSPIRE].
K. Jensen, More holographic Berezinskii-Kosterlitz-Thouless transitions, Phys. Rev. D 82 (2010) 046005 [arXiv:1006.3066] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
A. Karch, A. O’Bannon and E. Thompson, The stress-energy tensor of flavor fields from AdS/CFT, JHEP 04 (2009) 021 [arXiv:0812.3629] [INSPIRE].
L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B44S10 (1966) 1.
O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].
I. Kirsch and D. Vaman, The D3/D7 background and flavor dependence of Regge trajectories, Phys. Rev. D 72 (2005) 026007 [hep-th/0505164] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS type IIB interface solutions. I. Local solution and supersymmetric Janus, JHEP 06 (2007) 021 [arXiv:0705.0022] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS type IIB interface solutions. II. Flux solutions and multi-Janus, JHEP 06 (2007) 022 [arXiv:0705.0024] [INSPIRE].
O. Aharony, L. Berdichevsky, M. Berkooz and I. Shamir, Near-horizon solutions for D3-branes ending on 5-branes, Phys. Rev. D 84 (2011) 126003 [arXiv:1106.1870] [INSPIRE].
F. Bigazzi, R. Casero, A. Cotrone, E. Kiritsis and A. Paredes, Non-critical holography and four-dimensional CFT’s with fundamentals, JHEP 10 (2005) 012 [hep-th/0505140] [INSPIRE].
R. Casero, C. Núñez and A. Paredes, Towards the string dual of N = 1 SQCD-like theories, Phys. Rev. D 73 (2006) 086005 [hep-th/0602027] [INSPIRE].
D. Mateos, R.C. Myers and R.M. Thomson, Holographic viscosity of fundamental matter, Phys. Rev. Lett. 98 (2007) 101601 [hep-th/0610184] [INSPIRE].
F. Bigazzi, A.L. Cotrone and J. Tarrio, Charged D3-D7 plasmas: novel solutions, extremality and stability issues, JHEP 07 (2013) 074 [arXiv:1304.4802] [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
M. Turyn, The graviton propagator in maximally symmetric spaces, J. Math. Phys. 31 (1990) 669 [INSPIRE].
B. Allen and M. Turyn, An evaluation of the graviton propagator in de Sitter space, Nucl. Phys. B 292 (1987) 813 [INSPIRE].
P.G. Freund and M.A. Rubin, Dynamics of dimensional reduction, Phys. Lett. B 97 (1980) 233 [INSPIRE].
O. DeWolfe, D.Z. Freedman, S.S. Gubser, G.T. Horowitz and I. Mitra, Stability of AdS(p) × M (q) compactifications without supersymmetry, Phys. Rev. D 65 (2002) 064033 [hep-th/0105047] [INSPIRE].
K. Jensen and A. O’Bannon, to appear.
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
E. D’Hoker, D.Z. Freedman and L. Rastelli, AdS/CFT four point functions: how to succeed at z integrals without really trying, Nucl. Phys. B 562 (1999) 395 [hep-th/9905049] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
D.V. Fursaev, Quantum entanglement on boundaries, JHEP 07 (2013) 119 [arXiv:1305.2334] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
L.-Y. Hung, R.C. Myers and M. Smolkin, On holographic entanglement entropy and higher curvature gravity, JHEP 04 (2011) 025 [arXiv:1101.5813] [INSPIRE].
L. Vanzo, Black holes with unusual topology, Phys. Rev. D 56 (1997) 6475 [gr-qc/9705004] [INSPIRE].
D. Birmingham, Topological black holes in Anti-de Sitter space, Class. Quant. Grav. 16 (1999) 1197 [hep-th/9808032] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero energy states, JHEP 06 (1999) 036 [hep-th/9906040] [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: 1307.5325
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Chang, HC., Karch, A. Entanglement entropy for probe branes. J. High Energ. Phys. 2014, 180 (2014). https://doi.org/10.1007/JHEP01(2014)180
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2014)180