Abstract
We construct charged black branes in type IIA flux compactifications that are dual to (2 + 1)-dimensional field theories at finite density. The internal space is a general Calabi-Yau manifold with fluxes, with internal dimensions much smaller than the AdS radius. Gauge fields descend from the 3-form RR potential evaluated on harmonic forms of the Calabi-Yau, and Kaluza-Klein modes decouple. Black branes are described by a four-dimensional effective field theory that includes only a few light fields and is valid over a parametrically large range of scales. This effective theory determines the low energy dynamics, stability and thermodynamic properties. Tools from flux compactifications are also used to construct holographic CFTs with no relevant scalar operators, that can lead to symmetric phases of condensed matter systems stable to very low temperatures. The general formalism is illustrated with simple examples such as toroidal compactifications and manifolds with a single size modulus. We initiate the classification of holographic phases of matter described by flux compactifications, which include generalized Reissner-Nordstrom branes, nonsupersymmetric \( Ad{S_2}\times {{\mathbb{R}}^2} \) and hyperscaling violating solutions.
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References
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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].
S. Sachdev, What can gauge-gravity duality teach us about condensed matter physics?, Ann. Rev. Condensed Matter Phys. 3 (2012) 9 [arXiv:1108.1197] [INSPIRE].
R. Cooper et al., Anomalous criticality in the electrical resistivity of La 2−x Sr x CuO 4, Science 323 (2009) 603.
N.E. Hussey, Topical review: phenomenology of the normal state in-plane transport properties of high-T c cuprates, Journal of Physics Condensed Matter 20 (2008) 123201 [arXiv:0804.2984].
G. Stewart, Non-Fermi-liquid behavior in d- and f-electron metals, Rev. Mod. Phys. 73 (2001) 797 [Addendum ibid. 78 (2006) 743] [INSPIRE].
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 [hep-th/9905111] [INSPIRE].
P.G. Freund and M.A. Rubin, Dynamics of dimensional reduction, Phys. Lett. B 97 (1980) 233 [INSPIRE].
A.R. Frey, Warped strings: selfdual flux and contemporary compactifications, hep-th/0308156 [INSPIRE].
E. Silverstein, TASI/PiTP/ISS lectures on moduli and microphysics, hep-th/0405068 [INSPIRE].
T.W. Grimm and J. Louis, The effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys. B 718 (2005) 153 [hep-th/0412277] [INSPIRE].
M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].
F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [INSPIRE].
O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [INSPIRE].
J. Polchinski and E. Silverstein, Dual purpose landscaping tools: small extra dimensions in AdS/CFT, arXiv:0908.0756 [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].
T.W. Grimm and J. Louis, The effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys. B 718 (2005) 153 [hep-th/0412277] [INSPIRE].
P. Candelas and X. de la Ossa, Moduli space of Calabi-Yau manifolds, Nucl. Phys. B 355 (1991) 455 [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].
C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Emergent quantum near-criticality from baryonic black branes, JHEP 03 (2010) 093 [arXiv:0911.0400] [INSPIRE].
I.R. Klebanov, S.S. Pufu and T. Tesileanu, Membranes with topological charge and AdS 4 /CFT 3 correspondence, Phys. Rev. D 81 (2010) 125011 [arXiv:1004.0413] [INSPIRE].
N. Benishti, D. Rodriguez-Gomez and J. Sparks, Baryonic symmetries and M5 branes in the AdS 4 /CFT 3 correspondence, JHEP 07 (2010) 024 [arXiv:1004.2045] [INSPIRE].
A. Donos and J.P. Gauntlett, Supersymmetric quantum criticality supported by baryonic charges, JHEP 10 (2012) 120 [arXiv:1208.1494] [INSPIRE].
S.B. Giddings and A. Maharana, Dynamics of warped compactifications and the shape of the warped landscape, Phys. Rev. D 73 (2006) 126003 [hep-th/0507158] [INSPIRE].
G. Shiu, G. Torroba, B. Underwood and M.R. Douglas, Dynamics of warped flux compactifications, JHEP 06 (2008) 024 [arXiv:0803.3068] [INSPIRE].
M.R. Douglas, Effective potential and warp factor dynamics, JHEP 03 (2010) 071 [arXiv:0911.3378] [INSPIRE].
S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007) 066001 [arXiv:0704.1160] [INSPIRE].
S.A. Hartnoll and C.P. Herzog, Ohm’s Law at strong coupling: s duality and the cyclotron resonance, Phys. Rev. D 76 (2007) 106012 [arXiv:0706.3228] [INSPIRE].
B. de Wit and I. Herger, Anti-de Sitter supersymmetry, Lect. Notes Phys. 541 (2000) 79 [hep-th/9908005] [INSPIRE].
J.P. Conlon, The QCD axion and moduli stabilisation, JHEP 05 (2006) 078 [hep-th/0602233] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
A. Fayyazuddin and M. Spalinski, Large-N superconformal gauge theories and supergravity orientifolds, Nucl. Phys. B 535 (1998) 219 [hep-th/9805096] [INSPIRE].
O. Aharony, A. Fayyazuddin and J.M. Maldacena, The large-N limit of N = 2, N = 1 field theories from three-branes in F-theory, JHEP 07 (1998) 013 [hep-th/9806159] [INSPIRE].
M. Fabinger and E. Silverstein, D-Sitter space: causal structure, thermodynamics and entropy, JHEP 12 (2004) 061 [hep-th/0304220] [INSPIRE].
E. Silverstein, AdS and dS entropy from string junctions: or, the function of junction conjunctions, in From fields to strings, volume 3, M. Shifman et al. eds., World Scientific, Singapore (2005), pg. 1848 [hep-th/0308175] [INSPIRE].
O. Aharony, Y.E. Antebi and M. Berkooz, On the conformal field theory duals of type IIA AdS 4 flux compactifications, JHEP 02 (2008) 093 [arXiv:0801.3326] [INSPIRE].
T. Banks and K. van den Broek, Massive IIA flux compactifications and U-dualities, JHEP 03 (2007) 068 [hep-th/0611185] [INSPIRE].
E. Witten, SL(2, Z) action on three-dimensional conformal field theories with Abelian symmetry, in From fields to strings, volume 2, M. Shifman et al. eds., World Scientific, Singapore (2005), pg. 1173 [hep-th/0307041] [INSPIRE].
S. Reffert, Toroidal orbifolds: resolutions, orientifolds and applications in string phenomenology, hep-th/0609040 [INSPIRE].
R. Blumenhagen, L. Görlich and T. Ott, Supersymmetric intersecting branes on the type IIA \( {{{{T^6}}} \left/ {{{{\mathbb{Z}}_4}}} \right.} \) orientifold, JHEP 01 (2003) 021 [hep-th/0211059] [INSPIRE].
M. Ihl and T. Wrase, Towards a realistic type IIA \( {{{{T^6}}} \left/ {{{{\mathbb{Z}}_4}}} \right.} \) orientifold model with background fluxes. Part 1. Moduli stabilization, JHEP 07 (2006) 027 [hep-th/0604087] [INSPIRE].
R. Flauger, S. Paban, D. Robbins and T. Wrase, Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes, Phys. Rev. D 79 (2009) 086011 [arXiv:0812.3886] [INSPIRE].
S. Kachru and E. Silverstein, 4D conformal theories and strings on orbifolds, Phys. Rev. Lett. 80 (1998) 4855 [hep-th/9802183] [INSPIRE].
Calabi-Yau manifold explorer webpage, http://cyexplorer.benjaminjurke.net/.
M.R. Douglas, J. Shelton and G. Torroba, Warping and supersymmetry breaking, arXiv:0704.4001 [INSPIRE].
M.R. Douglas and G. Torroba, Kinetic terms in warped compactifications, JHEP 05 (2009) 013 [arXiv:0805.3700] [INSPIRE].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of charged dilaton black holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].
K. Goldstein et al., Holography of dyonic dilaton black branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].
C. Charmousis, B. Gouteraux, B. Kim, E. Kiritsis and R. Meyer, Effective holographic theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
S.S. Gubser and F.D. Rocha, Peculiar properties of a charged dilatonic black hole in AdS 5, Phys. Rev. D 81 (2010) 046001 [arXiv:0911.2898] [INSPIRE].
E. Perlmutter, Domain wall holography for finite temperature scaling solutions, JHEP 02 (2011) 013 [arXiv:1006.2124] [INSPIRE].
G. Bertoldi, B.A. Burrington and A.W. Peet, Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries, Phys. Rev. D 82 (2010) 106013 [arXiv:1007.1464] [INSPIRE].
G. Bertoldi, B.A. Burrington, A.W. Peet and I.G. Zadeh, Lifshitz-like black brane thermodynamics in higher dimensions, Phys. Rev. D 83 (2011) 126006 [arXiv:1101.1980] [INSPIRE].
P. Berglund, J. Bhattacharyya and D. Mattingly, Charged dilatonic AdS black branes in arbitrary dimensions, JHEP 08 (2012) 042 [arXiv:1107.3096] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
J.W. York, Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].
G. Gibbons and S. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
J.D. Brown and J.W. York Jr,, Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [INSPIRE].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].
G. Torroba and H. Wang, Local quantum criticality in string compactifications, work in progress.
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011) 065029 [arXiv:0903.2477] [INSPIRE].
M. Cubrovic, J. Zaanen and K. Schalm, String theory, quantum phase transitions and the emergent Fermi-liquid, Science 325 (2009) 439 [arXiv:0904.1993] [INSPIRE].
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [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].
E. Shaghoulian, Holographic entanglement entropy and Fermi surfaces, JHEP 05 (2012) 065 [arXiv:1112.2702] [INSPIRE].
D.S. Fisher, Scaling and critical slowing down in random-field Ising systems, Phys. Rev. Lett. 56 (1986) 416 [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].
P. Dey and S. Roy, Lifshitz-like space-time from intersecting branes in string/M theory, JHEP 06 (2012) 129 [arXiv:1203.5381] [INSPIRE].
M. Ammon, M. Kaminski and A. Karch, Hyperscaling-violation on probe D-branes, JHEP 11 (2012) 028 [arXiv:1207.1726] [INSPIRE].
E. Perlmutter, Hyperscaling violation from supergravity, JHEP 06 (2012) 165 [arXiv:1205.0242] [INSPIRE].
M. Alishahiha, E. O Colgain and H. Yavartanoo, Charged black branes with hyperscaling violating factor, JHEP 11 (2012) 137 [arXiv:1209.3946] [INSPIRE].
N. Iizuka, N. Kundu, P. Narayan and S.P. Trivedi, Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity, JHEP 01 (2012) 094 [arXiv:1105.1162] [INSPIRE].
J. Bhattacharya, S. Cremonini and A. Sinkovics, On the IR completion of geometries with hyperscaling violation, JHEP 02 (2013) 147 [arXiv:1208.1752] [INSPIRE].
S. Cremonini and A. Sinkovics, Spatially modulated instabilities of geometries with hyperscaling violation, arXiv:1212.4172 [INSPIRE].
N. Iizuka and K. Maeda, Stripe instabilities of geometries with hyperscaling violation, Phys. Rev. D 87 (2013) 126006 [arXiv:1301.5677] [INSPIRE].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
R. Gregory and R. Laflamme, The instability of charged black strings and p-branes, Nucl. Phys. B 428 (1994) 399 [hep-th/9404071] [INSPIRE].
S.S. Gubser and I. Mitra, Instability of charged black holes in anti-de Sitter space, hep-th/0009126 [INSPIRE].
S.S. Gubser and I. Mitra, The evolution of unstable black holes in anti-de Sitter space, JHEP 08 (2001) 018 [hep-th/0011127] [INSPIRE].
D. Anninos, T. Anous, J. Barandes, F. Denef and B. Gaasbeek, Hot halos and galactic glasses, JHEP 01 (2012) 003 [arXiv:1108.5821] [INSPIRE].
D. Anninos, T. Anous, F. Denef, G. Konstantinidis and E. Shaghoulian, Supergoop dynamics, JHEP 03 (2013) 081 [arXiv:1205.1060] [INSPIRE].
N. Iizuka et al., Bianchi attractors: a classification of extremal black brane geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].
N. Iizuka et al., Extremal horizons with reduced symmetry: hyperscaling violation, stripes and a classification for the homogeneous case, JHEP 03 (2013) 126 [arXiv:1212.1948] [INSPIRE].
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Torroba, G., Wang, H. Black branes in flux compactifications. J. High Energ. Phys. 2013, 126 (2013). https://doi.org/10.1007/JHEP10(2013)126
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DOI: https://doi.org/10.1007/JHEP10(2013)126