Abstract
We study the instability, for the supersymmetric Yang-Mills (SYM) theories, caused by the external electric field through the imaginary part of the action of the D7 probe brane, which is embedded in the background of type IIB theory. This instability is related to the Schwinger effect, namely to the quark pair production due to the external electric field, for the SU(N c ) SYM theories. In this holographic approach, it is possible to calculate the Schwinger effect for various phases of the theories. Here we give the calculation for \( \mathcal{N}=2 \) SYM theory and the analysis is extended to the finite temperature deconfinement and the zero temperature confinement phases of the Yang-Mills (YM) theory. By comparing the obtained production rates with the one of the supersymmetric case, the dynamical quark mass is estimated and we find how it varies with the chiral condensate. Based on this analysis, we give a speculation on the extension of the Nambu-Jona-Lasinio model to the finite temperature YM theory, and four fermi coupling is evaluated in the confinement theory.
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References
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [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. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Towards a holographic dual of large-N c QCD, JHEP 05 (2004) 041 [hep-th/0311270] [INSPIRE].
J. Babington, J. Erdmenger, N.J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in nonsupersymmetric gauge / gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
A. O’Bannon, Hall Conductivity of Flavor Fields from AdS/CFT, Phys. Rev. D 76 (2007) 086007 [arXiv:0708.1994] [INSPIRE].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Quarks in an external electric field in finite temperature large-N gauge theory, JHEP 08 (2008) 092 [arXiv:0709.1554] [INSPIRE].
J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, JHEP 12 (2007) 091 [arXiv:0709.1551] [INSPIRE].
N.J. Evans and J.P. Shock, Chiral dynamics from AdS space, Phys. Rev. D 70 (2004) 046002 [hep-th/0403279] [INSPIRE].
C. Núñez, A. Paredes and A.V. Ramallo, Flavoring the gravity dual of N = 1 Yang-Mills with probes, JHEP 12 (2003) 024 [hep-th/0311201] [INSPIRE].
K. Ghoroku and M. Yahiro, Chiral symmetry breaking driven by dilaton, Phys. Lett. B 604 (2004) 235 [hep-th/0408040] [INSPIRE].
R. Casero, C. Núñez and A. Paredes, Towards the string dual of N = 1 SQCD-like theories, Phys. Rev. D 73 (2006) 086005 [hep-th/0602027] [INSPIRE].
A. Karch, A. O’Bannon and K. Skenderis, Holographic renormalization of probe D-branes in AdS/CFT, JHEP 04 (2006) 015 [hep-th/0512125] [INSPIRE].
K. Hashimoto and T. Oka, Vacuum Instability in Electric Fields via AdS/CFT: Euler-Heisenberg Lagrangian and Planckian Thermalization, JHEP 10 (2013) 116 [arXiv:1307.7423] [INSPIRE].
K. Hashimoto, T. Oka and A. Sonoda, Magnetic instability in AdS/CFT: Schwinger effect and Euler-Heisenberg Lagrangian of supersymmetric QCD, JHEP 06 (2014) 085 [arXiv:1403.6336] [INSPIRE].
X. Wu, Notes on holographic Schwinger effect, JHEP 09 (2015) 044 [arXiv:1507.03208] [INSPIRE].
J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].
G.W. Semenoff and K. Zarembo, Holographic Schwinger Effect, Phys. Rev. Lett. 107 (2011) 171601 [arXiv:1109.2920] [INSPIRE].
Y. Sato and K. Yoshida, Holographic Schwinger effect in confining phase, JHEP 09 (2013) 134 [arXiv:1306.5512] [INSPIRE].
K. Ghoroku, T. Sakaguchi, N. Uekusa and M. Yahiro, Flavor quark at high temperature from a holographic model, Phys. Rev. D 71 (2005) 106002 [hep-th/0502088] [INSPIRE].
K. Ghoroku, M. Ishihara and T. Taminato, Holographic Confining Gauge theory and Response to Electric Field, Phys. Rev. D 81 (2010) 026001 [arXiv:0909.5522] [INSPIRE].
D. Mateos, R.C. Myers and R.M. Thomson, Thermodynamics of the brane, JHEP 05 (2007) 067 [hep-th/0701132] [INSPIRE].
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I, Phys. Rev. 122 (1961) 345 [INSPIRE].
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev. 124 (1961) 246 [INSPIRE].
S.P. Klevansky, The Nambu-Jona-Lasinio model of quantum chromodynamics, Rev. Mod. Phys. 64 (1992) 649 [INSPIRE].
A.A. Osipov, B. Hiller, J. Moreira, A.H. Blin and J. da Providencia, Lowering the critical temperature with eight-quark interactions, Phys. Lett. B 646 (2007) 91 [hep-ph/0612082] [INSPIRE].
M. Kobayashi, H. Kondo and T. Maskawa, Symmetry breaking of the chiral U(3) ⊗ U(3) and the quark model, Prog. Theor. Phys. 45 (1971) 1955 [INSPIRE].
A.O. Starinets, Quasinormal modes of near extremal black branes, Phys. Rev. D 66 (2002) 124013 [hep-th/0207133] [INSPIRE].
P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
J. Mas, J.P. Shock and J. Tarrio, Holographic Spectral Functions in Metallic AdS/CFT, JHEP 09 (2009) 032 [arXiv:0904.3905] [INSPIRE].
C. Hoyos-Badajoz, K. Landsteiner and S. Montero, Holographic meson melting, JHEP 04 (2007) 031 [hep-th/0612169] [INSPIRE].
N. Evans and E. Threlfall, Mesonic quasinormal modes of the Sakai-Sugimoto model at high temperature, Phys. Rev. D 77 (2008) 126008 [arXiv:0802.0775] [INSPIRE].
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Ghoroku, K., Ishihara, M. Holographic Schwinger effect and chiral condensate in SYM theory. J. High Energ. Phys. 2016, 11 (2016). https://doi.org/10.1007/JHEP09(2016)011
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DOI: https://doi.org/10.1007/JHEP09(2016)011