Superfluid and metamagnetic phase transitions in ω-deformed gauged supergravity

Open Access
Regular Article - Theoretical Physics

Abstract

We study non-supersymmetric truncations of ω-deformed \( \mathcal{N}=8 \) gauged supergravity that retain a U(1) gauge field and three scalars, of which two are neutral and one charged. We construct dyonic domain-wall and black hole solutions with AdS4 boundary conditions when only one (neutral) scalar is non-vanishing, and examine their behavior as the magnetic field and temperature of the system are varied. In the infrared the domain-wall solutions approach either dyonic \( {\mathrm{AdS}}_2\times {\mathbb{R}}^2 \) or else Lifshitz-like, hyperscaling violating geometries. The scaling exponents of the latter are z = 3/2 and θ = −2, and are independent of the ω-deformation. New ω-dependent AdS4 vacua are also identified. We find a rich structure for the magnetization of the system, including a line of metamagnetic first-order phase transitions when the magnetic field lies in a particular range. Such transitions arise generically in the ω-deformed theories. Finally, we study the onset of a superfluid phase by allowing a fluctuation of the charged scalar field to condense, spontaneously breaking the abelian gauge symmetry. The mechanism by which the superconducting instability ceases to exist for strong magnetic fields is different depending on whether the field is positive or negative. Finally, such instabilities are expected to compete with spatially modulated phases.

Keywords

AdS-CFT Correspondence Supergravity Models 

Notes

Open Access

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References

  1. [1]
    G. Dall’Agata, G. Inverso and M. Trigiante, Evidence for a family of SO(8) gauged supergravity theories, Phys. Rev. Lett. 109 (2012) 201301 [arXiv:1209.0760] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    B. de Wit and H. Nicolai, Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions, JHEP 05 (2013) 077 [arXiv:1302.6219] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    T. Fischbacher, K. Pilch and N.P. Warner, New Supersymmetric and Stable, Non-Supersymmetric Phases in Supergravity and Holographic Field Theory, arXiv:1010.4910 [INSPIRE].
  4. [4]
    B. de Wit and H. Nicolai, N=8 Supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  7. [7]
    B. Gouteraux and E. Kiritsis, Generalized Holographic Quantum Criticality at Finite Density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  8. [8]
    P. Bueno, W. Chemissany and C.S. Shahbazi, On hvLif -like solutions in gauged Supergravity, Eur. Phys. J. C 74 (2014) 2684 [arXiv:1212.4826] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    B. Gouteraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, JHEP 04 (2013) 053 [arXiv:1212.2625] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    G. Lifschytz and M. Lippert, Holographic Magnetic Phase Transition, Phys. Rev. D 80 (2009) 066007 [arXiv:0906.3892] [INSPIRE].ADSGoogle Scholar
  11. [11]
    E. D’Hoker and P. Kraus, Holographic Metamagnetism, Quantum Criticality and Crossover Behavior, JHEP 05 (2010) 083 [arXiv:1003.1302] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    O. Bergman, J. Erdmenger and G. Lifschytz, A Review of Magnetic Phenomena in Probe-Brane Holographic Matter, Lect. Notes Phys. 871 (2013) 591 [arXiv:1207.5953] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    A. Donos, J.P. Gauntlett, J. Sonner and B. Withers, Competing orders in M-theory: superfluids, stripes and metamagnetism, JHEP 03 (2013) 108 [arXiv:1212.0871] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].ADSGoogle Scholar
  15. [15]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].ADSGoogle Scholar
  18. [18]
    H. Ooguri and C.-S. Park, Holographic End-Point of Spatially Modulated Phase Transition, Phys. Rev. D 82 (2010) 126001 [arXiv:1007.3737] [INSPIRE].ADSGoogle Scholar
  19. [19]
    A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  20. [20]
    A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  21. [21]
    J Chang et al., Direct observation of competition between superconductivity and charge density wave order in Y Ba 2 Cu 3 O 6.67, Nature Phys. 8 (2012) 871.ADSCrossRefGoogle Scholar
  22. [22]
    S.S. Gubser and A. Nellore, Ground states of holographic superconductors, Phys. Rev. D 80 (2009) 105007 [arXiv:0908.1972] [INSPIRE].ADSGoogle Scholar
  23. [23]
    G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    J. Bhattacharya, S. Cremonini and B. Goutéraux, Intermediate scalings in holographic RG flows and conductivities, JHEP 02 (2015) 035 [arXiv:1409.4797] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    A. Ito et al., Study of Ising system Fe x Mn 1−x TiO 3 with exchange frustrations by observing magnetization process, J. Magnet. Magnet. Mater. 104-107 (1992) 1635.CrossRefGoogle Scholar
  26. [26]
    K. Kaczmarsca et al., Magnetic, resistivity and ESR studies of the compounds GdNi 2 Sb 2 and GdCu 2 Sb 2, J. Magnet. Magnet. Mater. 147 (1995) 81.ADSCrossRefGoogle Scholar
  27. [27]
    S.A. Grigera et al., Magnetic field-tuned quantum criticality in the metallic ruthenate Sr 3 Ru 2 O 7, Science 294 (2001) 329.ADSCrossRefGoogle Scholar
  28. [28]
    C. Krey et al., First order metamagnetic transition in Ho 2 T i 2 O 7 observed by vibrating coil magnetometry at milli-Kelvin temperatures, Phys. Rev. Lett. 108 (2012) 257204.ADSCrossRefGoogle Scholar
  29. [29]
    H. Lü, Y. Pang and C.N. Pope, AdS Dyonic Black Hole and its Thermodynamics, JHEP 11 (2013) 033 [arXiv:1307.6243] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    H. Lü, Y. Pang and C.N. Pope, An ω deformation of gauged STU supergravity, JHEP 04 (2014) 175 [arXiv:1402.1994] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    T. Hertog and K. Maeda, Black holes with scalar hair and asymptotics in N = 8 supergravity, JHEP 07 (2004) 051 [hep-th/0404261] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    A. Ashtekar and A. Magnon, Asymptotically anti-de Sitter space-times, Class. Quant. Grav. 1 (1984) L39 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: Conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  34. [34]
    S. Cremonini and A. Sinkovics, Spatially Modulated Instabilities of Geometries with Hyperscaling Violation, JHEP 01 (2014) 099 [arXiv:1212.4172] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    N. Iizuka and K. Maeda, Stripe Instabilities of Geometries with Hyperscaling Violation, Phys. Rev. D 87 (2013) 126006 [arXiv:1301.5677] [INSPIRE].ADSGoogle Scholar
  36. [36]
    S. Cremonini, Spatially Modulated Instabilities for Scaling Solutions at Finite Charge Density, arXiv:1310.3279 [INSPIRE].
  37. [37]
    A. Borghese, G. Dibitetto, A. Guarino, D. Roest and O. Varela, The SU(3)-invariant sector of new maximal supergravity, JHEP 03 (2013) 082 [arXiv:1211.5335] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and AstronomyTexas A&M UniversityCollege StationUnited States
  2. 2.DAMTP, Centre for Mathematical SciencesCambridge UniversityCambridgeUnited Kingdom

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