La correspondance AdS/CFT est utile pour l’´etude des th´eories des champs fortement coupl´ees. Comme nous l’avons vu plus haut, on peut admettre que cette dualit´e s’applique `a une classe de th´eories plus larges que celles donn´ees par la th´eorie des cordes et la
physique des D-branes. Cela nous a permis de construire des mod`eles holographiques simples bas´es sur la th´eorie d’Einstein-Maxwell. La correspondance AdS/CFT a cepen-dant aussi ´et´e fortement ´etudi´ee dans une approche plus math´ematique, dans le contexte de la th´eorie des cordes.
Dans l’exemple de la th´eorie des cordes de type IIB sur l’espace AdS5 ⇥ S5, il n’y a
pas de s´eparation d’´echelle entre les di↵´erents multiplets chiraux r´esultants de la
com-pactification des champs dix-dimensionnels sur la sph`ere S5. Ceci est dˆu `a la courbure
non-nulle de l’espace AdS. Il est cependant possible d’´ecrire une action pour le multiplet gravitationnel, qui contient notamment la m´etrique 5-dimensionnelle et les champs duaux aux courants conserv´es de la th´eorie des champs duale. Cette action `a 5 dimensions
cor-respond `a la th´eorie de supergravit´e N = 8 `a 5 dimensions. On pense que cette th´eorie
est une troncation consistante de la th´eorie des cordes de type IIB sur AdS5⇥ S5 dans le
sens o`u chaque solution classique de cette th´eorie `a 5 dimensions correspond (peut ˆetre
‘uplift´ee’) `a une solution dans la th´eorie 10-dimensionnelle.
Les th´eories de supergravit´e jaug´ee sont int´eressantes pour l’holographie car elles
ad-mettent des solutions asymptotiquement AdS. Ceci est dˆu au fait que le potentiel pour les
champs scalaires est non-nul, celui-ci joue le rˆole d’une constante cosmologique n´egative. Dans cette th`ese nous nous sommes particuli`erement int´eress´es `a la th´eorie de
super-gravit´e jaug´ee N = 2 en 4 dimensions, qui est une troncation consistante de la th´eorie
de supergravit´e jaug´ee N = 8 obtenue par de Wit et Nicolai. Cette derni`ere est une
troncation consistante de la th´eorie M sur la sph`ere S7.
Nous nous sommes int´eress´es `a un mod`ele STU simple de la supergravit´e jaug´eeN = 2
en 4 dimensions. Cette th´eorie contient le multiplet gravitationnel et trois multiplets vectoriels. Lorsque les couplages au champ de jauge sont de type Fayet-Iliopoulos, le lagrangien est donn´e par le lagrangien de la th´eorie non-jaug´ee auquel s’ajoute un potentiel
pour les champs scalaires. Nous avons consid´er´e le cas o`u l’espace des modules est le coset
(aussi appel´e espace homog`ene) [SL(2,R)/U(1)]3.
Nous avons montr´e que cette th´eorie admet un groupe de dualit´e U (1)3 dont les
trans-formations du sous-groupe U (1)2 pr´eservent les ´equations BPS. Nous avons appliqu´e les
transformations de ce sous-groupe de dualit´e pour g´en´erer de nouvelles solutions de trous noirs supersym´etriques analytiques `a partir des solutions connues. Pour les trous noirs statiques, nous avons g´en´eralis´e les solutions analytiques de Cacciatori et Klemm qui comportent trois charges magn´etiques. En plus de ces trois charges magn´etiques, nos so-lutions admettent aussi deux charges ´electriques et correspondent donc `a des trous noirs dyoniques. Pour les trous noirs en rotation, nous avons g´en´eralis´e les solutions connues `a deux param`etres en y ajoutant un param`etre suppl´ementaire qui repr´esente un mode normalisable scalaire.
Bibliography
[1] F. Nitti, G. Policastro, and T. Vanel, “Dressing the Electron Star in a Holographic Superconductor,” JHEP 1310 (2013) 019, arXiv:1307.4558 [hep-th].
[2] F. Nitti, G. Policastro, and T. Vanel, “Polarized solutions and Fermi surfaces in holographic Bose-Fermi systems,” arXiv:1407.0410 [hep-th].
[3] N. Halmagyi and T. Vanel, “AdS Black Holes from Duality in Gauged Supergravity,” JHEP 1404 (2014) 130, arXiv:1312.5430 [hep-th]. [4] J. M. Maldacena, “The Large N limit of superconformal field theories and
supergravity,” Adv.Theor.Math.Phys. 2 (1998) 231–252, arXiv:hep-th/9711200 [hep-th].
[5] G. ’t Hooft, “A Planar Diagram Theory for Strong Interactions,” Nucl.Phys. B72 (1974) 461.
[6] J. Polchinski, “Dirichlet Branes and Ramond-Ramond charges,” Phys.Rev.Lett. 75 (1995) 4724–4727, arXiv:hep-th/9510017 [hep-th].
[7] J. Dai, R. Leigh, and J. Polchinski, “New Connections Between String Theories,” Mod.Phys.Lett. A4 (1989) 2073–2083.
[8] O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, “Large N field theories, string theory and gravity,” Phys.Rept. 323 (2000) 183–386,
arXiv:hep-th/9905111 [hep-th].
[9] E. Witten, “Anti-de Sitter space and holography,” Adv.Theor.Math.Phys. 2 (1998) 253–291, arXiv:hep-th/9802150 [hep-th].
[10] M. Bianchi, D. Z. Freedman, and K. Skenderis, “Holographic renormalization,” Nucl.Phys. B631 (2002) 159–194, arXiv:hep-th/0112119 [hep-th].
[11] K. Skenderis, “Lecture notes on holographic renormalization,” Class.Quant.Grav. 19 (2002) 5849–5876, arXiv:hep-th/0209067 [hep-th].
[12] P. Breitenlohner and D. Z. Freedman, “Positive Energy in anti-De Sitter
Backgrounds and Gauged Extended Supergravity,” Phys.Lett. B115 (1982) 197. [13] P. Breitenlohner and D. Z. Freedman, “Stability in Gauged Extended
Supergravity,” Annals Phys. 144 (1982) 249.
[14] I. R. Klebanov and E. Witten, “AdS / CFT correspondence and symmetry breaking,” Nucl.Phys. B556 (1999) 89–114, arXiv:hep-th/9905104 [hep-th].
[15] 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 [hep-th].
[16] O. Aharony, O. Bergman, D. L. Ja↵eris, and J. Maldacena, “N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” JHEP 0810 (2008) 091, arXiv:0806.1218 [hep-th].
[17] E. Witten, “Anti-de Sitter space, thermal phase transition, and confinement in gauge theories,” Adv.Theor.Math.Phys. 2 (1998) 505–532, arXiv:hep-th/9803131 [hep-th].
[18] A. Karch and E. Katz, “Adding flavor to AdS / CFT,” JHEP 0206 (2002) 043, arXiv:hep-th/0205236 [hep-th].
[19] G. ’t Hooft, “Dimensional reduction in quantum gravity,” arXiv:gr-qc/9310026 [gr-qc].
[20] L. Susskind, “The World as a hologram,” J.Math.Phys. 36 (1995) 6377–6396, arXiv:hep-th/9409089 [hep-th].
[21] J. M. Luttinger and J. C. Ward, “Ground-state energy of a many-fermion system. ii,” Phys. Rev. 118 (Jun, 1960) 1417–1427.
http://link.aps.org/doi/10.1103/PhysRev.118.1417.
[22] J. M. Luttinger, “Fermi surface and some simple equilibrium properties of a system of interacting fermions,” Phys. Rev. 119 (Aug, 1960) 1153–1163. http://link.aps.org/doi/10.1103/PhysRev.119.1153.
[23] J. Bardeen, L. Cooper, and J. Schrie↵er, “Microscopic theory of superconductivity,” Phys.Rev. 106 (1957) 162.
[24] J. Bardeen, L. Cooper, and J. Schrie↵er, “Theory of superconductivity,” Phys.Rev. 108 (1957) 1175–1204.
[25] S. A. Hartnoll, “Lectures on holographic methods for condensed matter physics,” Class.Quant.Grav. 26 (2009) 224002, arXiv:0903.3246 [hep-th].
[26] S. Sachdev, “Quantum magnetism and criticality,” Nature Physics 4 (Mar., 2008) 173–185, arXiv:0711.3015 [cond-mat.str-el].
[27] S. A. Hartnoll, “Horizons, holography and condensed matter,” arXiv:1106.4324 [hep-th].
[28] J. Bednorz and K. Muller, “Possible high Tc superconductivity in the Ba-La-Cu-O system,” Z.Phys. B64 (1986) 189–193.
[29] S. Sachdev and B. Keimer, “Quantum criticality,” Physics Today 64 no. 2, (2011) 29, arXiv:1102.4628 [cond-mat.str-el].
[30] S. Sachdev, “Condensed Matter and AdS/CFT,” Lect.Notes Phys. 828 (2011) 273–311, arXiv:1002.2947 [hep-th].
[31] G. Gibbons and S. Hawking, “Action Integrals and Partition Functions in Quantum Gravity,” Phys.Rev. D15 (1977) 2752–2756.
[32] T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, “Emergent quantum criticality, Fermi surfaces, and AdS(2),” Phys.Rev. D83 (2011) 125002, arXiv:0907.2694 [hep-th].
[33] S. Sachdev, “Compressible quantum phases from conformal field theories in 2+1 dimensions,” Phys.Rev. D86 (2012) 126003, arXiv:1209.1637 [hep-th]. [34] H. Liu, J. McGreevy, and D. Vegh, “Non-Fermi liquids from holography,”
Phys.Rev. D83 (2011) 065029, arXiv:0903.2477 [hep-th].
[35] M. Cubrovic, J. Zaanen, and K. Schalm, “String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid,” Science 325 (2009) 439–444, arXiv:0904.1993 [hep-th].
[36] N. Iqbal, H. Liu, and M. Mezei, “Semi-local quantum liquids,” JHEP 1204 (2012) 086, arXiv:1105.4621 [hep-th].
[37] N. Iqbal, H. Liu, and M. Mezei, “Quantum phase transitions in semi-local quantum liquids,” arXiv:1108.0425 [hep-th].
[38] T. Faulkner, N. Iqbal, H. Liu, J. McGreevy, and D. Vegh, “Charge transport by holographic Fermi surfaces,” Phys.Rev. D88 (2013) 045016, arXiv:1306.6396 [hep-th].
[39] S. A. Hartnoll and A. Tavanfar, “Electron stars for holographic metallic criticality,” Phys.Rev. D83 (2011) 046003, arXiv:1008.2828 [hep-th]. [40] S. A. Hartnoll, J. Polchinski, E. Silverstein, and D. Tong, “Towards strange
metallic holography,” JHEP 1004 (2010) 120, arXiv:0912.1061 [hep-th]. [41] S. Kachru, X. Liu, and M. Mulligan, “Gravity duals of Lifshitz-like fixed points,”
Phys.Rev. D78 (2008) 106005, arXiv:0808.1725 [hep-th].
[42] G. T. Horowitz and B. Way, “Lifshitz Singularities,” Phys.Rev. D85 (2012) 046008, arXiv:1111.1243 [hep-th].
[43] S. A. Hartnoll, D. M. Hofman, and A. Tavanfar, “Holographically smeared Fermi surface: Quantum oscillations and Luttinger count in electron stars,”
Europhys.Lett. 95 (2011) 31002, arXiv:1011.2502 [hep-th].
[44] S. A. Hartnoll, D. M. Hofman, and D. Vegh, “Stellar spectroscopy: Fermions and holographic Lifshitz criticality,” JHEP 1108 (2011) 096, arXiv:1105.3197 [hep-th].
[45] S. El-Showk and K. Papadodimas, “Emergent Spacetime and Holographic CFTs,” JHEP 1210 (2012) 106, arXiv:1101.4163 [hep-th].
[46] S. A. Hartnoll and P. Petrov, “Electron star birth: A continuous phase transition at nonzero density,” Phys.Rev.Lett. 106 (2011) 121601, arXiv:1011.6469
[hep-th].
[47] A. Allais, J. McGreevy, and S. J. Suh, “A quantum electron star,” Phys.Rev.Lett. 108 (2012) 231602, arXiv:1202.5308 [hep-th].
[48] A. Allais and J. McGreevy, “How to construct a gravitating quantum electron star,” Phys.Rev. D88 no. 6, (2013) 066006, arXiv:1306.6075 [hep-th].
[49] S. S. Gubser, “Breaking an Abelian gauge symmetry near a black hole horizon,” Phys.Rev. D78 (2008) 065034, arXiv:0801.2977 [hep-th].
[50] G. T. Horowitz, “Theory of Superconductivity,” Lect.Notes Phys. 828 (2011) 313–347, arXiv:1002.1722 [hep-th].
[51] G. T. Horowitz and M. M. Roberts, “Zero Temperature Limit of Holographic Superconductors,” JHEP 0911 (2009) 015, arXiv:0908.3677 [hep-th]. [52] S. S. Gubser and A. Nellore, “Ground states of holographics,” Phys.Rev. D80
(2009) 105007, arXiv:0908.1972 [hep-th].
[53] S. A. Hartnoll, C. P. Herzog, and G. T. Horowitz, “Building a Holographic
Superconductor,” Phys.Rev.Lett. 101 (2008) 031601, arXiv:0803.3295 [hep-th]. [54] S. A. Hartnoll, C. P. Herzog, and G. T. Horowitz, “Holographic Superconductors,”
JHEP 0812 (2008) 015, arXiv:0810.1563 [hep-th].
[55] T. Albash and C. V. Johnson, “A Holographic Superconductor in an External Magnetic Field,” JHEP 0809 (2008) 121, arXiv:0804.3466 [hep-th].
[56] S. A. Hartnoll and L. Huijse, “Fractionalization of holographic Fermi surfaces,” Class.Quant.Grav. 29 (2012) 194001, arXiv:1111.2606 [hep-th].
[57] A. Adam, B. Crampton, J. Sonner, and B. Withers, “Bosonic Fractionalisation Transitions,” JHEP 1301 (2013) 127, arXiv:1208.3199 [hep-th].
[58] B. Gouteraux and E. Kiritsis, “Quantum critical lines in holographic phases with (un)broken symmetry,” JHEP 1304 (2013) 053, arXiv:1212.2625 [hep-th]. [59] T. Hartman and S. A. Hartnoll, “Cooper pairing near charged black holes,” JHEP
1006 (2010) 005, arXiv:1003.1918 [hep-th].
[60] Y. Liu, K. Schalm, Y.-W. Sun, and J. Zaanen, “BCS instabilities of electron stars to holographic superconductors,” JHEP 1405 (2014) 122, arXiv:1404.0571 [hep-th].
[61] M. Edalati, K. W. Lo, and P. W. Phillips, “Neutral Order Parameters in Metallic Criticality in d=2+1 from a Hairy Electron Star,” Phys.Rev. D84 (2011) 066007, arXiv:1106.3139 [hep-th].
[62] Y. Liu, K. Schalm, Y.-W. Sun, and J. Zaanen, “Bose-Fermi competition in holographic metals,” JHEP 1310 (2013) 064, arXiv:1307.4572 [hep-th]. [63] L. D. Landau and E. M. Lifshitz, Quantum mechanics: non-relativistic theory.
Elsevier, 1977.
[64] M. Oshikawa, “Topological Approach to Luttinger’s Theorem and the Fermi Surface of a Kondo Lattice,” Physical Review Letters 84 (Apr., 2000) 3370–3373, cond-mat/0002392.
[65] T. Hartman and S. A. Hartnoll, “Cooper pairing near charged black holes,” JHEP 1006 (2010) 005, arXiv:1003.1918 [hep-th].
[66] P. Basu, J. He, A. Mukherjee, M. Rozali, and H.-H. Shieh, “Competing Holographic Orders,” JHEP 1010 (2010) 092, arXiv:1007.3480 [hep-th]. [67] A. Donos, J. P. Gauntlett, J. Sonner, and B. Withers, “Competing orders in M-theory: superfluids, stripes and metamagnetism,” JHEP 1303 (2013) 108, arXiv:1212.0871 [hep-th].
[68] D. Musso, “Competition/Enhancement of Two Probe Order Parameters in the Unbalanced Holographic Superconductor,” JHEP 1306 (2013) 083,
arXiv:1302.7205 [hep-th].
[69] R.-G. Cai, L. Li, L.-F. Li, and Y.-Q. Wang, “Competition and Coexistence of Order Parameters in Holographic Multi-Band Superconductors,” JHEP 1309 (2013) 074, arXiv:1307.2768 [hep-th].
[70] Z.-Y. Nie, R.-G. Cai, X. Gao, and H. Zeng, “Competition between the s-wave and p-wave superconductivity phases in a holographic model,” JHEP 1311 (2013) 087, arXiv:1309.2204 [hep-th].
[71] I. Amado, D. Arean, A. Jimenez-Alba, L. Melgar, and I. Salazar Landea, “Holographic s+p Superconductors,” Phys.Rev. D89 (2014) 026009, arXiv:1309.5086 [hep-th].
[72] A. Donos, J. P. Gauntlett, and C. Pantelidou, “Competing p-wave orders,” Class.Quant.Grav. 31 (2014) 055007, arXiv:1310.5741 [hep-th].
[73] L.-F. Li, R.-G. Cai, L. Li, and Y.-Q. Wang, “The competition between s-wave order and d-wave order in holographic superconductors,” arXiv:1405.0382 [hep-th].
[74] M. Cubrovic, Y. Liu, K. Schalm, Y.-W. Sun, and J. Zaanen, “Spectral probes of the holographic Fermi groundstate: dialing between the electron star and AdS Dirac hair,” Phys.Rev. D84 (2011) 086002, arXiv:1106.1798 [hep-th]. [75] B. de Wit and H. Nicolai, “N=8 Supergravity,” Nucl.Phys. B208 (1982) 323. [76] S. L. Cacciatori and D. Klemm, “Supersymmetric AdS(4) black holes and
attractors,” JHEP 1001 (2010) 085, arXiv:0911.4926 [hep-th].
[77] D. Klemm, “Rotating BPS black holes in matter-coupled AdS4 supergravity,”
JHEP 1107 (2011) 019, arXiv:1103.4699 [hep-th].
[78] J. M. Maldacena and C. Nunez, “Supergravity description of field theories on curved manifolds and a no go theorem,” Int. J. Mod. Phys. A16 (2001) 822–855, hep-th/0007018.
[79] C. Nunez, I. Park, M. Schvellinger, and T. A. Tran, “Supergravity duals of gauge theories from F(4) gauged supergravity in six-dimensions,” JHEP 0104 (2001) 025, arXiv:hep-th/0103080 [hep-th].
[80] J. P. Gauntlett, N. Kim, S. Pakis, and D. Waldram, “Membranes wrapped on holomorphic curves,” Phys.Rev. D65 (2002) 026003, arXiv:hep-th/0105250 [hep-th].
[81] S. Cucu, H. Lu, and J. F. Vazquez-Poritz, “A Supersymmetric and smooth compactification of M theory to AdS(5),” Phys.Lett. B568 (2003) 261–269, arXiv:hep-th/0303211 [hep-th].
[82] S. Cucu, H. Lu, and J. F. Vazquez-Poritz, “Interpolating from AdS(D-2) x S**2 to AdS(D),” Nucl.Phys. B677 (2004) 181–222, arXiv:hep-th/0304022 [hep-th]. [83] I. Bah, C. Beem, N. Bobev, and B. Wecht, “Four-Dimensional SCFTs from
M5-Branes,” JHEP 1206 (2012) 005, arXiv:1203.0303 [hep-th].
[84] A. Almuhairi and J. Polchinski, “Magnetic AdS x R2: Supersymmetry and
stability,” arXiv:1108.1213 [hep-th].
[85] F. Benini and N. Bobev, “Two-dimensional SCFTs from wrapped branes and c-extremization,” JHEP 1306 (2013) 005, arXiv:1302.4451 [hep-th].
[86] J. P. Gauntlett, “Branes, calibrations and supergravity,” arXiv:hep-th/0305074 [hep-th].
[87] M. M. Caldarelli and D. Klemm, “Supersymmetry of Anti-de Sitter black holes,” Nucl.Phys. B545 (1999) 434–460, arXiv:hep-th/9808097 [hep-th].
[88] D. Klemm and W. Sabra, “Supersymmetry of black strings in D = 5 gauged supergravities,” Phys.Rev. D62 (2000) 024003, arXiv:hep-th/0001131 [hep-th]. [89] R. P. Geroch, “A Method for generating solutions of Einstein’s equations,”
J.Math.Phys. 12 (1971) 918–924.
[90] L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara, et al., “General matter coupled N=2 supergravity,” Nucl.Phys. B476 (1996) 397–417,
arXiv:hep-th/9603004 [hep-th].
[91] B. de Wit and H. Nicolai, “N=8 supergravity with local so(8) x su(8) invariance,” Phys. Lett. B108 (1982) 285.
[92] M. J. Du↵ and J. T. Liu, “Anti-de sitter black holes in gauged n = 8 supergravity,” Nucl. Phys. B554 (1999) 237–253, hep-th/9901149.
[93] M. Cvetic, M. Du↵, P. Hoxha, J. T. Liu, H. Lu, et al., “Embedding AdS black holes in ten-dimensions and eleven-dimensions,” Nucl.Phys. B558 (1999) 96–126, arXiv:hep-th/9903214 [hep-th].
[94] H. Nicolai and K. Pilch, “Consistent Truncation of d = 11 Supergravity on
AdS4⇥ S7,” JHEP 1203 (2012) 099, arXiv:1112.6131 [hep-th].
[95] B. de Wit and H. Nicolai, “The Consistency of the S**7 Truncation in D=11 Supergravity,” Nucl. Phys. B281 (1987) 211.
[96] G. Dall’Agata and A. Gnecchi, “Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity,” JHEP 1103 (2011) 037, arXiv:1012.3756
[97] B. de Wit and A. Van Proeyen, “Special geometry, cubic polynomials and homogeneous quaternionic spaces,” Commun. Math. Phys. 149 (1992) 307–334, arXiv:hep-th/9112027.
[98] B. de Wit, F. Vanderseypen, and A. Van Proeyen, “Symmetry structure of special geometries,” Nucl.Phys. B400 (1993) 463–524, arXiv:hep-th/9210068 [hep-th]. [99] R. Corrado, M. Gunaydin, N. P. Warner, and M. Zagermann, “Orbifolds and flows
from gauged supergravity,” Phys. Rev. D65 (2002) 125024, arXiv:hep-th/0203057.
[100] A. Gnecchi and N. Halmagyi, “Supersymmetric black holes in AdS4 from very
special geometry,” JHEP 1404 (2014) 173, arXiv:1312.2766 [hep-th]. [101] N. Halmagyi, “BPS Black Hole Horizons in N=2 Gauged Supergravity,” JHEP
1402 (2014) 051, arXiv:1308.1439 [hep-th].
[102] A. Gnecchi, K. Hristov, D. Klemm, C. Toldo, and O. Vaughan, “Rotating black holes in 4d gauged supergravity,” JHEP 1401 (2014) 127, arXiv:1311.1795 [hep-th].
[103] N. Halmagyi, M. Petrini, and A. Za↵aroni, “BPS black holes in AdS4 from
M-theory,” JHEP 1308 (2013) 124, arXiv:1305.0730 [hep-th].
[104] D. D. K. Chow and G. Comp`ere, “Dyonic AdS black holes in maximal gauged supergravity,” Phys.Rev. D89 (2014) 065003, arXiv:1311.1204 [hep-th]. [105] V. A. Kostelecky and M. J. Perry, “Solitonic black holes in gauged N=2
supergravity,” Phys.Lett. B371 (1996) 191–198, arXiv:hep-th/9512222 [hep-th].
[106] M. Cvetic, G. Gibbons, H. Lu, and C. Pope, “Rotating black holes in gauged supergravities: Thermodynamics, supersymmetric limits, topological solitons and time machines,” arXiv:hep-th/0504080 [hep-th].
[107] D. Klemm and O. Vaughan, “Nonextremal black holes in gauged supergravity and the real formulation of special geometry,” JHEP 1301 (2013) 053,
arXiv:1207.2679 [hep-th].
[108] A. Gnecchi and C. Toldo, “On the non-BPS first order flow in N=2 U(1)-gauged Supergravity,” JHEP 1303 (2013) 088, arXiv:1211.1966 [hep-th].
[109] K. Hristov, C. Toldo, and S. Vandoren, “Phase transitions of magnetic AdS4 black holes with scalar hair,” Phys.Rev. D88 (2013) 026019, arXiv:1304.5187
[hep-th].
[110] A. Anabalon and D. Astefanesei, “On attractor mechanism of AdS4 black holes,”
Phys.Lett. B727 (2013) 568–572, arXiv:1309.5863 [hep-th].
[111] A. Anabalon and D. Astefanesei, “Black holes in !-defomed gauged N = 8 supergravity,” Phys.Lett. B732 (2014) 137–141, arXiv:1311.7459 [hep-th]. [112] H. Lu, Y. Pang, and C. Pope, “AdS Dyonic Black Hole and its Thermodynamics,”
[113] O. Lunin and J. M. Maldacena, “Deforming field theories with u(1) x u(1) global symmetry and their gravity duals,” JHEP 05 (2005) 033, hep-th/0502086. [114] S. Frolov, “Lax pair for strings in Lunin-Maldacena background,” JHEP 0505
(2005) 069, arXiv:hep-th/0503201 [hep-th].
[115] O. Aharony, B. Kol, and S. Yankielowicz, “On exactly marginal deformations of N=4 SYM and type IIB supergravity on AdS(5) x S**5,” JHEP 0206 (2002) 039, arXiv:hep-th/0205090 [hep-th].
[116] R. G. Leigh and M. J. Strassler, “Exactly marginal operators and duality in four-dimensional n=1 supersymmetric gauge theory,” Nucl. Phys. B447 (1995) 95–136, hep-th/9503121.
[117] M. Berkooz and B. Pioline, “5D Black Holes and Non-linear Sigma Models,” JHEP 0805 (2008) 045, arXiv:0802.1659 [hep-th].
[118] O. Bergman, J. Erdmenger, and G. Lifschytz, “A Review of Magnetic Phenomena in Probe-Brane Holographic Matter,” Lect.Notes Phys. 871 (2013) 591–624, arXiv:1207.5953 [hep-th].
[119] G. T. Horowitz, J. E. Santos, and D. Tong, “Optical Conductivity with Holographic Lattices,” JHEP 1207 (2012) 168, arXiv:1204.0519 [hep-th]. [120] G. T. Horowitz and J. E. Santos, “General Relativity and the Cuprates,”
arXiv:1302.6586 [hep-th].
[121] D. Vegh, “Holography without translational symmetry,” arXiv:1301.0537 [hep-th].
[122] M. Taylor, “Non-relativistic holography,” arXiv:0812.0530 [hep-th]. [123] P. Horava, “Membranes at Quantum Criticality,” JHEP 03 (2009) 020,
arXiv:arXiv:0812.4287 [hep-th].
[124] P. Horava, “Quantum Gravity at a Lifshitz Point,” Phys. Rev. D79 (2009) 084008, arXiv:arXiv:0901.3775 [hep-th].
[125] T. Griffin, P. Horava, and C. M. Melby-Thompson, “Lifshitz Gravity for Lifshitz Holography,” Phys.Rev.Lett. 110 no. 8, (2013) 081602, arXiv:1211.4872
[hep-th].
[126] D. Son, “Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry,” Phys.Rev. D78 (2008) 046003, arXiv:0804.3972 [hep-th].
[127] K. Balasubramanian and J. McGreevy, “Gravity duals for non-relativistic CFTs,” Phys.Rev.Lett. 101 (2008) 061601, arXiv:0804.4053 [hep-th].
[128] C. P. Herzog, M. Rangamani, and S. F. Ross, “Heating up Galilean holography,” JHEP 0811 (2008) 080, arXiv:0807.1099 [hep-th].
[129] J. Maldacena, D. Martelli, and Y. Tachikawa, “Comments on string theory backgrounds with non-relativistic conformal symmetry,” JHEP 0810 (2008) 072, arXiv:0807.1100 [hep-th].
[130] A. Adams, K. Balasubramanian, and J. McGreevy, “Hot Spacetimes for Cold Atoms,” JHEP 0811 (2008) 059, arXiv:0807.1111 [hep-th].
[131] K. Balasubramanian and K. Narayan, “Lifshitz spacetimes from AdS null and cosmological solutions,” JHEP 08 (2010) 014, arXiv:1005.3291 [hep-th]. [132] A. Donos and J. P. Gauntlett, “Lifshitz Solutions of D=10 and D=11
supergravity,” JHEP 1012 (2010) 002, arXiv:1008.2062 [hep-th]. [133] A. Donos, J. P. Gauntlett, N. Kim, and O. Varela, “Wrapped M5-branes,
consistent truncations and AdS/CMT,” JHEP 1012 (2010) 003, arXiv:1009.3805 [hep-th].
[134] R. Gregory, S. L. Parameswaran, G. Tasinato, and I. Zavala, “Lifshitz solutions in supergravity and string theory,” JHEP 1012 (2010) 047, arXiv:1009.3445 [hep-th].
[135] N. Halmagyi, M. Petrini, and A. Za↵aroni, “Non-Relativistic Solutions of N=2 Gauged Supergravity,” JHEP 1108 (2011) 041, arXiv:1102.5740 [hep-th]. [136] D. Cassani and A. F. Faedo, “Constructing Lifshitz solutions from AdS,” JHEP
1105 (2011) 013, arXiv:1102.5344 [hep-th].
[137] F. Bigazzi, A. L. Cotrone, J. Mas, A. Paredes, A. V. Ramallo, et al., “D3-D7 Quark-Gluon Plasmas,” JHEP 0911 (2009) 117, arXiv:0909.2865 [hep-th]. [138] F. Bigazzi, A. L. Cotrone, J. Mas, D. Mayerson, and J. Tarrio, “D3-D7
Quark-Gluon Plasmas at Finite Baryon Density,” JHEP 1104 (2011) 060, arXiv:1101.3560 [hep-th].
[139] U. Gursoy, E. Kiritsis, L. Mazzanti, G. Michalogiorgakis, and F. Nitti, “Improved Holographic QCD,” Lect.Notes Phys. 828 (2011) 79–146, arXiv:1006.5461 [hep-th].
[140] S. Bhattacharyya, V. E. Hubeny, S. Minwalla, and M. Rangamani, “Nonlinear Fluid Dynamics from Gravity,” JHEP 02 (2008) 045, arXiv:arXiv:0712.2456 [hep-th].
[141] Y. Neiman and Y. Oz, “Relativistic Hydrodynamics with General Anomalous Charges,” JHEP 1103 (2011) 023, arXiv:1011.5107 [hep-th].
[142] I. Bredberg, C. Keeler, V. Lysov, and A. Strominger, “From Navier-Stokes To Einstein,” JHEP 1207 (2012) 146, arXiv:1101.2451 [hep-th].
[143] D. T. Son and A. O. Starinets, “Minkowski space correlators in AdS / CFT correspondence: Recipe and applications,” JHEP 0209 (2002) 042,
arXiv:hep-th/0205051 [hep-th].
[144] C. Herzog and D. Son, “Schwinger-Keldysh propagators from AdS/CFT correspondence,” JHEP 0303 (2003) 046, arXiv:hep-th/0212072 [hep-th]. [145] R. Kubo, “Statistical mechanical theory of irreversible processes. 1. General theory
and simple applications in magnetic and conduction problems,” J.Phys.Soc.Jap. 12 (1957) 570–586.
[146] B. de Wit and A. Van Proeyen, “Hidden symmetries, special geometry and quaternionic manifolds,” Int.J.Mod.Phys. D3 (1994) 31–48,