Abstract
We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction of fundamental strings ending on a stack of D3-branes and smeared uniformly in the three spatial directions along the D3-branes. These automatically include a distribution of D5-brane baryon vertices necessary to soak up string charge. The backgrounds are static, preserving eight supersymmetries, an SO(5) global symmetry and symmetry under spatial translations and rotations. We obtain the most general BPS configurations consistent with the symmetries. We show that the solutions to the Type IIB field equations are completely specified by a single function (the dilaton) satisfying a Poisson-like equation in two dimensions. We further find that the equation admits a class of solutions displaying Lifshitz-like scaling with dynamical critical exponent z = 7. The equations also admit an asymptotically AdS5 × S5 solution deformed by the presence of backreacted string sources that yield a uniform density of heavy quarks in \( \mathcal{N}=4 \) SYM.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Grinstein, Anisotropic sine-Gordon model and infinite-order phase transitions in three dimensions, Phys. Rev. B 23 (1981) 4615.
R.M. Hornreich, M. Luban and S. Shtrikman, Critical Behavior at the Onset of k -Space Instability on the lamda Line, Phys. Rev. Lett. 35 (1975) 1678 [INSPIRE].
S. Sachdev, Quantum Phase Transitions, Cambridge University Press, (1999).
E. Fradkin, Field Theories of Condensed Matter Physics, Cambridge University Press, (2013).
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [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].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [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].
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].
E. Witten, Baryons and branes in anti-de Sitter space, JHEP 07 (1998) 006 [hep-th/9805112] [INSPIRE].
A.F. Faedo, B. Fraser and S.P. Kumar, Supersymmetric Lifshitz-like backgrounds from \( \mathcal{N}=4 \) SYM with heavy quark density, JHEP 02 (2014) 066 [arXiv:1310.0206] [INSPIRE].
K. Rajagopal and F. Wilczek, The condensed matter physics of QCD, hep-ph/0011333 [INSPIRE].
K. Fukushima and T. Hatsuda, The phase diagram of dense QCD, Rept. Prog. Phys. 74 (2011) 014001 [arXiv:1005.4814] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618 [INSPIRE].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [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].
G.P. Korchemsky and A.V. Radyushkin, Infrared factorization, Wilson lines and the heavy quark limit, Phys. Lett. B 279 (1992) 359 [hep-ph/9203222] [INSPIRE].
S.P. Kumar, Heavy quark density in N = 4 SYM: from hedgehog to Lifshitz spacetimes, JHEP 08 (2012) 155 [arXiv:1206.5140] [INSPIRE].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
T. Azeyanagi, W. Li and T. Takayanagi, On String Theory Duals of Lifshitz-like Fixed Points, JHEP 06 (2009) 084 [arXiv:0905.0688] [INSPIRE].
A.F. Faedo, A. Kundu, D. Mateos and J. Tarrio, (Super) Yang-Mills at Finite Heavy-Quark Density, JHEP 02 (2015) 010 [arXiv:1410.4466] [INSPIRE].
N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].
S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05 (2006) 037 [hep-th/0603208] [INSPIRE].
J. Gomis and F. Passerini, Holographic Wilson Loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].
S.A. Hartnoll and S.P. Kumar, Higher rank Wilson loops from a matrix model, JHEP 08 (2006) 026 [hep-th/0605027] [INSPIRE].
S. Yamaguchi, Bubbling geometries for half BPS Wilson lines, Int. J. Mod. Phys. A 22 (2007) 1353 [hep-th/0601089] [INSPIRE].
O. Lunin, On gravitational description of Wilson lines, JHEP 06 (2006) 026 [hep-th/0604133] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Gravity duals of half-BPS Wilson loops, JHEP 06 (2007) 063 [arXiv:0705.1004] [INSPIRE].
J.P. Gauntlett, J.B. Gutowski, C.M. Hull, S. Pakis and H.S. Reall, All supersymmetric solutions of minimal supergravity in five-dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [INSPIRE].
J.P. Gauntlett, J.B. Gutowski and S. Pakis, The geometry of D = 11 null Killing spinors, JHEP 12 (2003) 049 [hep-th/0311112] [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of M-theory, Class. Quant. Grav. 21 (2004) 4335 [hep-th/0402153] [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].
H. Singh, Lifshitz/Schródinger Dp-branes and dynamical exponents, JHEP 07 (2012) 082 [arXiv:1202.6533] [INSPIRE].
H. Singh, Lifshitz to AdS flow with interpolating p-brane solutions, JHEP 08 (2013) 097 [arXiv:1305.3784] [INSPIRE].
P. Dey and S. Roy, Lifshitz-like space-time from intersecting branes in string/M theory, JHEP 06 (2012) 129 [arXiv:1203.5381] [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].
D. Gaiotto and J. Maldacena, The gravity duals of N = 2 superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [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].
M. Headrick, Hedgehog black holes and the Polyakov loop at strong coupling, Phys. Rev. D 77 (2008) 105017 [arXiv:0712.4155] [INSPIRE].
F. Benini, F. Canoura, S. Cremonesi, C. Núñez and A.V. Ramallo, Unquenched flavors in the Klebanov-Witten model, JHEP 02 (2007) 090 [hep-th/0612118] [INSPIRE].
F. Benini, F. Canoura, S. Cremonesi, C. Núñez and A.V. Ramallo, Backreacting flavors in the Klebanov-Strassler background, JHEP 09 (2007) 109 [arXiv:0706.1238] [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].
F. Bigazzi, A.L. Cotrone, J. Mas, D. Mayerson and J. Tarrio, D3-D7 quark-gluon Plasmas at Finite Baryon Density, JHEP 04 (2011) 060 [arXiv:1101.3560] [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].
H.-Y. Chen, K. Hashimoto and S. Matsuura, Towards a Holographic Model of Color-Flavor Locking Phase, JHEP 02 (2010) 104 [arXiv:0909.1296] [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].
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: 1412.7274
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
Faedo, A.F., Fraser, B. & Kumar, S.P. Emergent Lifshitz scaling from \( \mathcal{N}=4 \) SYM with supersymmetric heavy-quark density. J. High Energ. Phys. 2015, 84 (2015). https://doi.org/10.1007/JHEP05(2015)084
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2015)084