Abstract
Within the framework of AdS/CFT duality, excited states of the conformal field living at the global AdS boundary of a four-dimensional spacetime Einstein gravity are investigated analytically in the probe limit where the field equations are linearized. At asymptotically large values, the threshold chemical potential for the appearance of excited condensate states are discrete, equal spacing, with the gap approaches zero logarithmically in the limit T → 0. Remarkably, numerical results show that, this behavior applies even for states as low as for the first or the second excited state of the condensate. This is especially significant on the liquid side of the black hole van der Waals-like phase transition (small or zero topological charge) where there seems to be no gap between the ground state and the first excited state at zero temperature. We postulate that, at the exact limit T = 0 where the gap is zero, the spectrum of threshold chemical potentials becomes continuous, all excited states of the condensate are activated above a finite chemical potential, suggesting a new quantum phase transition as a function of the chemical potential. Previous studies have largely missed this continuous spectrum of excited states in the T → 0 limit. This fact should be taken into account carefully in AdS/CFT duality studies.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.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].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
P. Basu, A. Mukherjee and H.-H. Shieh, Supercurrent: vector hair for an AdS black hole, Phys. Rev. D 79 (2009) 045010 [arXiv:0809.4494] [INSPIRE].
C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [INSPIRE].
S.S. Gubser, Colorful horizons with charge in anti-de Sitter space, Phys. Rev. Lett. 101 (2008) 191601 [arXiv:0803.3483] [INSPIRE].
Y.-Q. Wang, T.-T. Hu, Y.-X. Liu, J. Yang and L. Zhao, Excited states of holographic superconductors, JHEP 06 (2020) 013 [arXiv:1910.07734] [INSPIRE].
Y. Bao, H. Guo and X.-M. Kuang, Excited states of holographic superconductor with scalar field coupled to Gauss-Bonnet invariance, Phys. Lett. B 822 (2021) 136646 [INSPIRE].
J. Pan, X. Qiao, D. Wang, Q. Pan, Z.-Y. Nie and J. Jing, Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity with backreactions, Phys. Lett. B 823 (2021) 136755 [arXiv:2109.02207] [INSPIRE].
Y. Tian, A topological charge of black holes, Class. Quant. Grav. 36 (2019) 245001 [arXiv:1804.00249] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Enthalpy and the mechanics of AdS black holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].
D. Kubizňák, R.B. Mann and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav. 34 (2017) 063001 [arXiv:1608.06147] [INSPIRE].
M. Ammon and J. Erdmenger, Gauge/gravity duality: foundations and applications, Cambridge University Press, Cambridge, U.K. (2015).
T.H. Phat and T.T. Nguyen, On the holographic phase transitions at finite topological charge, Eur. Phys. J. C 81 (2021) 428 [arXiv:2004.12192] [INSPIRE].
G. Siopsis and J. Therrien, Analytic calculation of properties of holographic superconductors, JHEP 05 (2010) 013 [arXiv:1003.4275] [INSPIRE].
T.H. Phat and T.T. Nguyen, On the triplet of holographic phase transition, arXiv:2110.08757 [INSPIRE].
A.M. Essin and D.J. Griffiths, Quantum mechanics of the 1/x2 potential, Amer. J. Phys. 74 (2006) 109.
A. Zettl, Sturm-Liouville theory, American Mathematical Society, Providence, RI, U.S.A. (2010).
H.N.N. Yepez, C.A. Vargas and A.L.S. Brito, The one-dimensional hydrogen atom in momentum representation, Eur. J. Phys. 8 (1987) 189.
Y.-Q. Wang, H.-B. Li, Y.-X. Liu and Y. Zhong, Excited states of holographic superconductors with backreaction, Eur. Phys. J. C 81 (2021) 628 [arXiv:1911.04475] [INSPIRE].
C.A. Bayona and N.R.F. Braga, Anti-de Sitter boundary in Poincaré coordinates, Gen. Rel. Grav. 39 (2007) 1367 [hep-th/0512182] [INSPIRE].
P. Basu, C. Krishnan and P.N. Bala Subramanian, Phases of global AdS black holes, JHEP 06 (2016) 139 [arXiv:1602.07211] [INSPIRE].
J. Markeviciute and J.E. Santos, Hairy black holes in AdS5 × S5, JHEP 06 (2016) 096 [arXiv:1602.03893] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2109.02420
Rights and permissions
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.
About this article
Cite this article
Nguyen, T.T., Phat, T.H. Asymptotic critical behavior of holographic superconductor phase transition — the spectrum of excited states becomes continuous at T = 0. J. High Energ. Phys. 2022, 4 (2022). https://doi.org/10.1007/JHEP06(2022)004
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2022)004