Skip to main content
SpringerLink
Log in

Infrared behavior of scalar condensates in effective holographic theories

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We investigate the infrared behavior of the spectrum of scalar-dressed, asymptotically Anti de Sitter (AdS) black brane (BB) solutions of effective holographic models. These solutions describe scalar condensates in the dual field theories. We show that for zero charge density the ground state of these BBs must be degenerate with the AdS vacuum, must satisfy conformal boundary conditions for the scalar field and it is isolated from the continuous part of the spectrum. When a finite charge density is switched on, the ground state is not anymore isolated and the degeneracy is removed. Depending on the coupling functions, the new ground state may possibly be energetically preferred with respect to the extremal Reissner-Nordstrom AdS BB. We derive several properties of BBs near extremality and at finite temperature. As a check and illustration of our results we derive and discuss several analytic and numerical, BB solutions of Einstein-scalar-Maxwell AdS gravity with different coupling functions and different potentials. We also discuss how our results can be used for understanding holographic quantum critical points, in particular their stability and the associated quantum phase transitions leading to superconductivity or hyperscaling violation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].

    Article  ADS  Google Scholar 

  2. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].

    ADS  Google Scholar 

  4. C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].

    Google Scholar 

  5. S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. C. Charmousis, B. Gouteraux and J. Soda, Einstein-Maxwell-Dilaton theories with a Liouville potential, Phys. Rev. D 80 (2009) 024028 [arXiv:0905.3337] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  7. M. Cadoni, G. D’Appollonio and P. Pani, Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime, JHEP 03 (2010) 100 [arXiv:0912.3520] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. 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].

    MathSciNet  ADS  Google Scholar 

  10. K. Goldstein et al., Holography of Dyonic Dilaton Black Branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].

    Article  ADS  Google Scholar 

  11. 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].

    Article  ADS  Google Scholar 

  12. 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].

    ADS  Google Scholar 

  13. B. Gouteraux and E. Kiritsis, Generalized Holographic Quantum Criticality at Finite Density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].

    Article  ADS  Google Scholar 

  14. 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].

    Article  ADS  Google Scholar 

  15. M. Cadoni and P. Pani, Holography of charged dilatonic black branes at finite temperature, JHEP 04 (2011) 049 [arXiv:1102.3820] [INSPIRE].

    Article  ADS  Google Scholar 

  16. S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [INSPIRE].

  17. B.-H. Lee, D.-W. Pang and C. Park, A holographic model of strange metals, Int. J. Mod. Phys. A 26 (2011) 2279 [arXiv:1107.5822] [INSPIRE].

    ADS  Google Scholar 

  18. B.S. Kim, Schródinger holography with and without hyperscaling violation, JHEP 06 (2012) 116 [arXiv:1202.6062] [INSPIRE].

    Article  ADS  Google Scholar 

  19. 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].

    Article  ADS  Google Scholar 

  20. J.-P. Wu and H.-B. Zeng, Dynamic gap from holographic fermions in charged dilaton black branes, JHEP 04 (2012) 068 [arXiv:1201.2485] [INSPIRE].

    Article  ADS  Google Scholar 

  21. K. Hashimoto and N. Iizuka, A Comment on Holographic Luttinger Theorem, JHEP 07 (2012) 064 [arXiv:1203.5388] [INSPIRE].

    Article  ADS  Google Scholar 

  22. M. Ammon, M. Kaminski and A. Karch, Hyperscaling-Violation on Probe D-branes, JHEP 11 (2012) 028 [arXiv:1207.1726] [INSPIRE].

    Article  ADS  Google Scholar 

  23. N. Iizuka and K. Maeda, Study of Anisotropic Black Branes in Asymptotically anti-de Sitter, JHEP 07 (2012) 129 [arXiv:1204.3008] [INSPIRE].

    Article  ADS  Google Scholar 

  24. P. Dey and S. Roy, Intersecting D-branes and Lifshitz-like space-time, Phys. Rev. D 86 (2012) 066009 [arXiv:1204.4858] [INSPIRE].

    ADS  Google Scholar 

  25. C. Park, Membrane paradigm in the Einstein-dilaton theory, arXiv:1209.0842 [INSPIRE].

  26. Y.S. Myung and T. Moon, Quasinormal frequencies and thermodynamic quantities for the Lifshitz black holes, Phys. Rev. D 86 (2012) 024006 [arXiv:1204.2116] [INSPIRE].

    ADS  Google Scholar 

  27. A. Adam, B. Crampton, J. Sonner and B. Withers, Bosonic Fractionalisation Transitions, JHEP 01 (2013) 127 [arXiv:1208.3199] [INSPIRE].

    Article  ADS  Google Scholar 

  28. B. Gouteraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, JHEP 04 (2013) 053 [arXiv:1212.2625] [INSPIRE].

    Article  ADS  Google Scholar 

  29. A. Salvio, Holographic Superfluids and Superconductors in Dilaton-Gravity, JHEP 09 (2012) 134 [arXiv:1207.3800] [INSPIRE].

    Article  ADS  Google Scholar 

  30. M. Cadoni and S. Mignemi, Phase transition and hyperscaling violation for scalar Black Branes, JHEP 06 (2012) 056 [arXiv:1205.0412] [INSPIRE].

    Article  ADS  Google Scholar 

  31. M. Cadoni and M. Serra, Hyperscaling violation for scalar black branes in arbitrary dimensions, arXiv:1209.4484 [INSPIRE].

  32. N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi Surfaces and Entanglement Entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. 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].

    ADS  Google Scholar 

  34. J. Gath, J. Hartong, R. Monteiro and N.A. Obers, Holographic Models for Theories with Hyperscaling Violation, arXiv:1212.3263 [INSPIRE].

  35. K. Narayan, On Lifshitz scaling and hyperscaling violation in string theory, Phys. Rev. D 85 (2012) 106006 [arXiv:1202.5935] [INSPIRE].

    ADS  Google Scholar 

  36. K. Narayan, T. Takayanagi and S.P. Trivedi, AdS plane waves and entanglement entropy, JHEP 04 (2013) 051 [arXiv:1212.4328] [INSPIRE].

    Article  ADS  Google Scholar 

  37. K. Narayan, Non-conformal brane plane waves and entanglement entropy, arXiv:1304.6697 [INSPIRE].

  38. P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  39. T. Torii, K. Maeda and M. Narita, Scalar hair on the black hole in asymptotically anti-de Sitter space-time, Phys. Rev. D 64 (2001) 044007 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  40. T. Hertog, Towards a Novel no-hair Theorem for Black Holes, Phys. Rev. D 74 (2006) 084008 [gr-qc/0608075] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  41. M. Cadoni, S. Mignemi and M. Serra, Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field, Phys. Rev. D 84 (2011) 084046 [arXiv:1107.5979] [INSPIRE].

    ADS  Google Scholar 

  42. M. Cadoni, S. Mignemi and M. Serra, Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity, Phys. Rev. D 85 (2012) 086001 [arXiv:1111.6581] [INSPIRE].

    ADS  Google Scholar 

  43. T. Hertog and K. Maeda, Black holes with scalar hair and asymptotics in N = 8 supergravity, JHEP 07 (2004) 051 [hep-th/0404261] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].

  45. O. Aharony, M. Berkooz and E. Silverstein, Multiple trace operators and nonlocal string theories, JHEP 08 (2001) 006 [hep-th/0105309] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. M. Berkooz, A. Sever and A. Shomer, ’Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. D. Marolf and S.F. Ross, Boundary Conditions and New Dualities: Vector Fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. T. Hartman and L. Rastelli, Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT, JHEP 01 (2008) 019 [hep-th/0602106] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. L. Vecchi, Multitrace deformations, Gamow states and Stability of AdS/CFT, JHEP 04 (2011) 056 [arXiv:1005.4921] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. T. Hertog and G.T. Horowitz, Designer gravity and field theory effective potentials, Phys. Rev. Lett. 94 (2005) 221301 [hep-th/0412169] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. C. Martinez, R. Troncoso and J. Zanelli, Exact black hole solution with a minimally coupled scalar field, Phys. Rev. D 70 (2004) 084035 [hep-th/0406111] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  52. G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università di Cagliari and INFN, Sezione di Cagliari, Cittadella Universitaria, 09042, Monserrato, Italy

    Mariano Cadoni & Matteo Serra

  2. CENTRA, Departamento de Física, Instituto Superior Técnico, Universidade Técnica de Lisboa - UTL, Avenida Rovisco Pais 1, 1049, Lisboa, Portugal

    Paolo Pani

  3. Institute for Theory & Computation, Harvard-Smithsonian CfA, 60 Garden Street, Cambridge, MA, U.S.A.

    Paolo Pani

Authors
  1. Mariano Cadoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paolo Pani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matteo Serra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mariano Cadoni.

Additional information

ArXiv ePrint: 1304.3279

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cadoni, M., Pani, P. & Serra, M. Infrared behavior of scalar condensates in effective holographic theories. J. High Energ. Phys. 2013, 29 (2013). https://doi.org/10.1007/JHEP06(2013)029

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2013)029

Keywords

Search

Navigation