Abstract
We use holography to study d = 4, \( \mathcal{N}=4 \), SU(Nc) super Yang-Mills coupled to Nf ≪ Nc quark flavors. We place the theory at finite isospin density nI by turning on an isospin chemical potential μI = Mq, with Mq the quark mass. We also turn on two R-symmetry charge densities n1 = n2. We show that the ground state is a supersymmetric, superfluid, color superconductor, namely a finite-density state that preserves a fraction of supersymmetry in which part of the global symmetries and part of the gauge symmetries are spontaneously broken. The holographic description consists of Nf D7-brane probes in AdS5 × S5. The symmetry breaking is due to the dissolution of some D3-branes inside the D7-branes triggered by the electric field associated to the isospin charge. The massless spectrum contains Goldstone bosons and their fermionic superpartners. The massive spectrum contains long-lived, mesonic quasi-particles if nI ≪ μ 3I , and no quasi-particles otherwise. We discuss the possibility that, despite the presence of mass scales and charge densities in the theory, conformal and relativistic invariance arise as emergent symmetries in the infrared.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.G. Alford, K. Rajagopal and F. Wilczek, QCD at finite baryon density: Nucleon droplets and color superconductivity, Phys. Lett. B 422 (1998) 247 [hep-ph/9711395] [INSPIRE].
M.G. Alford, K. Rajagopal and F. Wilczek, Color flavor locking and chiral symmetry breaking in high density QCD, Nucl. Phys. B 537 (1999) 443 [hep-ph/9804403] [INSPIRE].
M.G. Alford, A. Schmitt, K. Rajagopal and T. Schäfer, Color superconductivity in dense quark matter, Rev. Mod. Phys. 80 (2008) 1455 [arXiv:0709.4635] [INSPIRE].
P. de Forcrand, Simulating QCD at finite density, PoS(LAT2009)010 (2009) [arXiv:1005.0539] [INSPIRE].
J.B. Kogut and D.K. Sinclair, The Finite temperature transition for 2-flavor lattice QCD at finite isospin density, Phys. Rev. D 70 (2004) 094501 [hep-lat/0407027] [INSPIRE].
D.T. Son and M.A. Stephanov, QCD at finite isospin density, Phys. Rev. Lett. 86 (2001) 592 [hep-ph/0005225] [INSPIRE].
D.T. Son and M.A. Stephanov, QCD at finite isospin density: From pion to quark-antiquark condensation, Phys. Atom. Nucl. 64 (2001) 834 [hep-ph/0011365] [INSPIRE].
D. Mateos, Gauge/string duality applied to heavy ion collisions: Limitations, insights and prospects, J. Phys. G 38 (2011) 124030 [arXiv:1106.3295] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, Cambridge University Press (2014) [arXiv:1101.0618] [INSPIRE].
A.F. Faedo, D. Mateos, C. Pantelidou and J. Tarrio, work in progress.
R. Harnik, D.T. Larson and H. Murayama, Supersymmetric color superconductivity, JHEP 03 (2004) 049 [hep-ph/0309224] [INSPIRE].
M. Arai and N. Okada, Color superconductivity in N = 2 supersymmetric gauge theories, Phys. Rev. D 74 (2006) 045004 [hep-th/0512234] [INSPIRE].
B.S. Rajput and S. Kumar, Color superconductivity in supersymmetric gauge theories, Int. J. Theor. Phys. 50 (2011) 1342 [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. Rozali, D. Smyth and E. Sorkin, Holographic Higgs Phases, JHEP 08 (2012) 118 [arXiv:1202.5271] [INSPIRE].
P. Basu, F. Nogueira, M. Rozali, J.B. Stang and M. Van Raamsdonk, Towards A Holographic Model of Color Superconductivity, New J. Phys. 13 (2011) 055001 [arXiv:1101.4042] [INSPIRE].
K. Bitaghsir Fadafan, J. Cruz Rojas and N. Evans, Holographic description of color superconductivity, Phys. Rev. D 98 (2018) 066010 [arXiv:1803.03107] [INSPIRE].
K. Ghoroku, K. Kashiwa, Y. Nakano, M. Tachibana and F. Toyoda, Color Superconductivity in Holographic SYM Theory, arXiv:1902.01093 [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
A. Hashimoto, The Shape of branes pulled by strings, Phys. Rev. D 57 (1998) 6441 [hep-th/9711097] [INSPIRE].
D. Bak, J.-H. Lee and H. Min, Dynamics of BPS states in the Dirac-Born-Infeld theory, Phys. Rev. D 59 (1999) 045011 [hep-th/9806149] [INSPIRE].
A.F. Faedo, D. Mateos, C. Pantelidou and J. Tarrio, Spectrum of a supersymmetric color superconductor, to appear.
J. Erdmenger, J. Grosse and Z. Guralnik, Spectral flow on the Higgs branch and AdS/CFT duality, JHEP 06 (2005) 052 [hep-th/0502224] [INSPIRE].
Z. Guralnik, S. Kovacs and B. Kulik, Holography and the Higgs branch of N = 2 SYM theories, JHEP 03 (2005) 063 [hep-th/0405127] [INSPIRE].
Z. Guralnik, Strong coupling dynamics of the Higgs branch: Rolling a Higgs by collapsing an instanton, Nucl. Phys. B 732 (2006) 46 [hep-th/0412074] [INSPIRE].
Z. Guralnik, S. Kovacs and B. Kulik, AdS/CFT duality and the Higgs branch of N = 2 SYM, Fortsch. Phys. 53 (2005) 480 [hep-th/0501154] [INSPIRE].
E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [INSPIRE].
M.R. Douglas, Branes within branes, NATO Sci. Ser. C 520 (1999) 267 [hep-th/9512077] [INSPIRE].
C.V. Johnson, D-brane primer, in Strings, branes and gravity. Proceedings, Theoretical Advanced Study Institute, TASI’99, Boulder, U.S.A., May 31-June 25, 1999, pp. 129-350 (2000) [https://doi.org/10.1142/9789812799630_0002] [hep-th/0007170] [INSPIRE].
A.F. Faedo, D. Mateos, C. Pantelidou and J. Tarrio, Unquenched flavor on the Higgs branch, JHEP 11 (2016) 021 [arXiv:1607.07773] [INSPIRE].
N.D. Lambert and D. Tong, Dyonic instantons in five-dimensional gauge theories, Phys. Lett. B 462 (1999) 89 [hep-th/9907014] [INSPIRE].
M. Zamaklar, Geometry of the nonAbelian DBI dyonic instanton, Phys. Lett. B 493 (2000) 411 [hep-th/0006090] [INSPIRE].
E. Eyras, P.K. Townsend and M. Zamaklar, The Heterotic dyonic instanton, JHEP 05 (2001) 046 [hep-th/0012016] [INSPIRE].
R. Apreda, J. Erdmenger, N. Evans and Z. Guralnik, Strong coupling effective Higgs potential and a first order thermal phase transition from AdS/CFT duality, Phys. Rev. D 71 (2005) 126002 [hep-th/0504151] [INSPIRE].
S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [INSPIRE].
S.S. Gubser, Thermodynamics of spinning D3-branes, Nucl. Phys. B 551 (1999) 667 [hep-th/9810225] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
M. Cvetič and S.S. Gubser, Phases of R charged black holes, spinning branes and strongly coupled gauge theories, JHEP 04 (1999) 024 [hep-th/9902195] [INSPIRE].
J. Erdmenger, M. Kaminski and F. Rust, Isospin diffusion in thermal AdS/CFT with flavor, Phys. Rev. D 76 (2007) 046001 [arXiv:0704.1290] [INSPIRE].
J. Erdmenger, M. Kaminski, P. Kerner and F. Rust, Finite baryon and isospin chemical potential in AdS/CFT with flavor, JHEP 11 (2008) 031 [arXiv:0807.2663] [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
A. Karch and A. O’Bannon, Holographic thermodynamics at finite baryon density: Some exact results, JHEP 11 (2007) 074 [arXiv:0709.0570] [INSPIRE].
D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite chemical potential, JHEP 11 (2007) 085 [arXiv:0709.1225] [INSPIRE].
B.I. Halperin, Dynamic properties of the multicomponent Bose fluid, Phys. Rev. B 11 (1975) 178.
H.B. Nielsen and S. Chadha, On How to Count Goldstone Bosons, Nucl. Phys. B 105 (1976) 445 [INSPIRE].
V.G. Filev, C.V. Johnson and J.P. Shock, Universal Holographic Chiral Dynamics in an External Magnetic Field, JHEP 08 (2009) 013 [arXiv:0903.5345] [INSPIRE].
I. Amado, D. Arean, A. Jimenez-Alba, K. Landsteiner, L. Melgar and I.S. Landea, Holographic Type II Goldstone bosons, JHEP 07 (2013) 108 [arXiv:1302.5641] [INSPIRE].
R. Argurio, A. Marzolla, A. Mezzalira and D. Naegels, Note on holographic nonrelativistic Goldstone bosons, Phys. Rev. D 92 (2015) 066009 [arXiv:1507.00211] [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. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [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].
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].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].
L. Thorlacius, Born-Infeld string as a boundary conformal field theory, Phys. Rev. Lett. 80 (1998) 1588 [hep-th/9710181] [INSPIRE].
T.J. Hollowood, S.P. Kumar, A. Naqvi and P. Wild, N = 4 SYM on S 3 with Near Critical Chemical Potentials, JHEP 08 (2008) 046 [arXiv:0803.2822] [INSPIRE].
T.J. Hollowood, S.P. Kumar and J.C. Myers, Weak coupling large-N transitions at finite baryon density, JHEP 11 (2011) 138 [arXiv:1110.0696] [INSPIRE].
I. Amado, D. Areán, A. Jiménez-Alba, K. Landsteiner, L. Melgar and I. Salazar Landea, Holographic Superfluids and the Landau Criterion, JHEP 02 (2014) 063 [arXiv:1307.8100] [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: 1807.09712
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Faedo, A.F., Mateos, D., Pantelidou, C. et al. A supersymmetric color superconductor from holography. J. High Energ. Phys. 2019, 106 (2019). https://doi.org/10.1007/JHEP05(2019)106
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2019)106