The core part of (5.62) is given by Z
d˜tdλdλ0 Γ(λ+ 1)Γ(−λ+ 1)
Γ(λ+ 1−d2 )Γ(1+d2 −λ)− Γ(λ+ 1)Γ(−λ+ 1) Γ(λ+1+d2 )Γ(1−d2 −λ)
!
× Γ(λ0+1+d2 )Γ(−λ0+1+d2 )
Γ(λ0 + 1)Γ(−λ0+ 1) × eλ˜tΓ(−λ+ 1+d2 )
Γ(−λ+ 1) −e−λt˜Γ(λ+1+d2 ) Γ(λ+ 1)
!
× eλ0˜t Γ(λ0+ 1)
Γ(λ0+ 1+d2 ) +e−λ0˜t Γ(−λ0+ 1) Γ(−λ0+ 1+d2 )
!
tλt0−λ0.
(B.16) Note that ˜t = ln(t +√
t2−1) ≥ 0. We introduce an upper cutoff T to regularize thet˜integral. With˜tintegrated out, (B.16) takes the following form
Z
dλdλ0 Γ(λ+ 1)Γ(−λ+ 1)
Γ(λ+1−d2 )Γ(1+d2 −λ) − Γ(λ+ 1)Γ(−λ+ 1) Γ(λ+ 1+d2 )Γ(1−d2 −λ)
!
× Γ(λ0+1+d2 )Γ(−λ0+1+d2 ) Γ(λ0 + 1)Γ(−λ0+ 1) tλt0−λ0
×
Γ(1+d2 −λ)Γ(λ0+1) Γ(1−λ)Γ(λ0+1+d2 )
e(λ+λ0)T−1
λ+λ0 + Γ(1+d2 −λ)Γ(1−λ0) Γ(−λ+ 1)Γ(−λ0 +1+d2 )
e(λ−λ0)T −1 λ−λ0
−Γ(λ+ 1+d2 )Γ(λ0+ 1) Γ(λ+ 1)Γ(λ0+1+d2 )
e(−λ+λ0)T−1
−λ+λ0 − Γ(λ+1+d2 )Γ(1−λ0) Γ(λ+ 1)Γ(1+d2 −λ0)
e(−λ−λ0)T−1
−λ−λ0
. (B.17) We now use the residue theorem to evaluate the integrals ofλandλ0. Note that the appearance of e(±λ±λ
0)T−1
±λ±λ0 does not introduce any new poles as they have finite limits when±λ±λ0 →0. We begin with the integral ofλ0. It is helpful to keep in mind thatt, t0 >1since the “mirror” does not leave the boundary untilt= 1. Completing theλ0 integral, we find only the first and third terms in the bracket contribute and the dependence on the cutoffT drops out naturally.
We obtain the result 2πi
Z
dλ Γ(λ+1)Γ(−λ+1)
Γ(λ+1−d2 )Γ(−λ+1+d2 )− Γ(λ+1)Γ(−λ+1) Γ(λ+1+d2 )Γ(−λ+1−d2 )
! tλ
×
∞
X
n=0
(−1)n n!Γ(1−n−1+d2 )
−t0−n−1+d2 λ+n+1+d2
Γ(1+d2 −λ)
Γ(1−λ) + t0−n−1+d2 n−λ+ 1+d2
Γ(λ+1+2d) Γ(λ+1)
. (B.18) We again perform the contour integral. This time it is much simpler: As t > 1, only the poles in the left half plane contribute. Considering the first term in the sum, we find that poles atλ+ 1 =−mform ∈ {0,1,2· · · }and λ+n+1+d2 = 0are relevant. The contribution from the first set of poles is proportional to
∞
X
m=0
(−1)mt−m−1 m! m+1−n−1+2d
1
Γ(1−d2 −m−1)− Γ(m+1+1+d2 )
Γ(m+1+1−d2 )Γ(1+d2 −m−1)
=
sin(π(3+2d))Γ(3+2d)
π − 1
Γ(−1−2d)
F
3+d
2 ,−n+1−d
2 ;−n+3−d 2 ,1
t
1 t(n+d−21).
(B.19) We note that thed-dependent prefactor vanishes identically by the properties of the Gamma function. The pole atλ+n+1+d2 = 0gives the contribution
∞
X
n=0
−(−1)n n!
1
Γ(−n−d) − Γ(1+d+n) Γ(1+n)Γ(−n)
(tt0)−n−1+d2 =− 1 Γ(−d)
(tt0)1+2d (tt0−1)1+d,
(B.20) where Γ(−d)1 cancels the overall divergent factorΓ(−d)to yield a finite numer-ical coefficient. Next we consider the second term in the sum of (B.18), the relevant poles are atλ+ 1+d2 =−m, with the contributions
∞
X
n,m=0
(−1)m+n m!n!
Γ(m+ 1+d2 + 1)
Γ(−n−1+d2 + 1)Γ(−m−d)Γ(m+ 1 +d)
t−m−1+d2 t0−n−1+2d m+n+ 1 +d
=
∞
X
n,m=0
(−1)m+n m!n!
sinπ(n+d−12 )Γ(n+1+d2 ) π
sinπ(m+d)Γ(m+ 1+d2 + 1) π
× t0−nt−m
m+n+ 1 +d(tt0)−1+d2
=
∞
X
n,m=0
sinπd−12 sinπd π2
Γ(1+d2 )Γ(3+d2 ) 1 +d
(1+d2 )n(3+d2 )m(1 +d)m+n
(2 +d)m+nm!n! (tt0)−1+d2 ,
where(α)m = Γ(α+m)Γ(α) is the Pochhammer symbol. The double sum can be expressed in terms of Appell function, which again can be converted to a Hypergeometric function
sinπd−12 sinπd π2
Γ(1+d2 )Γ(3+d2 ) 1 +d F1
1+d,3+d 2 ,1+d
2 ,2+d;1 t,1
t0
(tt0)−1+d2
= sinπd−12 sinπd π2
Γ(1+d2 )Γ(3+d2 ) 1 +d
1− 1
t0 −1−d
×F
1 +d,3 +d
2 ,2 +d; t0 −t (t0−1)t
(tt0)−1+d2 .
Writtingsin-functions as product of twoΓ-functions, collecting all nonvanish-ing terms and insertnonvanish-ing the overall factor, we end up with the follownonvanish-ing result
δφd(t)
δφ0(t0) =−Γ(1+d2 )2d−1 Γ(1−d2 )Γ(d)
− 1
(tt0−1)1+d + Γ(1+d2 )
2Γ(1−d2 )Γ(1 +d)F
1 +d,3 +d
2 ,2 +d; t0 −t (t0−1)t
1 (tt0 −t)1+d
. (B.21)
[1] M. Ammon, T. H. Ngo, and A. O’Bannon, Holographic Flavor Transport in Arbitrary Constant Background Fields, JHEP10(2009) 027, arXiv:0908.2625.
[2] J. Erdmenger, S. Lin, and T. H. Ngo, A moving mirror in AdS space as a toy model for holographic thermalization, JHEP04(2011) 035, arXiv:1101.5505.
[3] J. Erdmenger, V. Grass, P. Kerner, and T. H. Ngo, Holographic Superfluidity in Imbalanced Mixtures, arXiv:1103.4145.
[4] DONUTCollaboration, K. Kodamaet al., Observation of tau-neutrino interactions, Phys. Lett.B504(2001) 218–224, arXiv:hep-ex/0012035.
[5] B. Zwiebach,A First Course in String Theory. Cambridge University Press, second edition ed., 2009.
[6] J. Polchinski,String Theory, vol. I+II. Cambridge University Press, paperback ed., 2005.
[7] L. A. Anchordoqui, H. Goldberg, X. Huang, D. Lust, and T. R. Taylor, Stringy origin of Tevatron Wjj anomaly, arXiv:1104.2302.
[8] D. Lust, S. Stieberger, and T. R. Taylor, The LHC String Hunter’s Companion, Nucl. Phys.B808(2009) 1–52, arXiv:0807.3333.
[9] K. Becker, M. Becker, and J. H. Schwarz,String Theory and M-Theory.
Cambridge University Press, 2007.
[10] J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2(1998) 231–252, arXiv:hep-th/9711200.
[11] S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett.B428(1998) 105–114, arXiv:hep-th/9802109.
[12] E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math.
Phys.2(1998) 253–291, arXiv:hep-th/9802150.
[13] O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323(2000) 183–386, arXiv:hep-th/9905111.
[14] E. D’Hoker and D. Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, arXiv:hep-th/0201253.
[15] S. A. Hartnoll, C. P. Herzog, and G. T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett.101(2008) 031601, arXiv:0803.3295.
[16] S. A. Hartnoll, C. P. Herzog, and G. T. Horowitz, Holographic Superconductors, JHEP12(2008) 015, arXiv:0810.1563.
[17] M. Ammon, J. Erdmenger, M. Kaminski, and P. Kerner,
Superconductivity from gauge/gravity duality with flavor, Phys. Lett.
B680(2009) 516–520, arXiv:0810.2316.
[18] M. Ammon, J. Erdmenger, M. Kaminski, and P. Kerner, Flavor Superconductivity from Gauge/Gravity Duality, JHEP10(2009) 067, arXiv:0903.1864.
[19] S. A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav.26(2009) 224002, arXiv:0903.3246.
[20] C. P. Herzog, Lectures on Holographic Superfluidity and
Superconductivity, J. Phys.A42(2009) 343001, arXiv:0904.1975.
[21] G. T. Horowitz, Introduction to Holographic Superconductors, arXiv:1002.1722.
[22] J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys.2010(2010) 723105,
arXiv:0909.0518.
[23] M. Kaminski, Flavor Superconductivity and Superfluidity, arXiv:1002.4886.
[24] S. Sachdev,Quantum Phase Transitions. Cambridge University Press, paperback ed., 2001.
[25] K. Jensen, A. Karch, and E. G. Thompson, A Holographic Quantum Critical Point at Finite Magnetic Field and Finite Density, JHEP05 (2010) 015, arXiv:1002.2447.
[26] N. Evans, K. Jensen, and K.-Y. Kim, Non Mean-Field Quantum Critical Points from Holography, Phys. Rev.D82(2010) 105012, arXiv:1008.1889.
[27] K. Jensen, More Holographic Berezinskii-Kosterlitz-Thouless Transitions, Phys. Rev.D82(2010) 046005, arXiv:1006.3066.
[28] E. D’Hoker and P. Kraus, Magnetic Field Induced Quantum Criticality via new AsymptoticallyAdS5 Solutions, Class. Quant. Grav.27(2010) 215022, arXiv:1006.2573.
[29] BRAHMSCollaboration, I. Arseneet al., Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment, Nucl. Phys.A757(2005) 1–27, arXiv:nucl-ex/0410020.
[30] PHENIXCollaboration, K. Adcoxet al., Formation of dense partonic matter in relativistic nucleus nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration, Nucl. Phys.A757(2005) 184–283, arXiv:nucl-ex/0410003.
[31] B. B. Backet al., The PHOBOS perspective on discoveries at RHIC, Nucl. Phys.A757(2005) 28–101, arXiv:nucl-ex/0410022.
[32] G. Policastro, D. T. Son, and A. O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev.
Lett.87(2001) 081601, arXiv:hep-th/0104066.
[33] P. Kovtun, D. T. Son, and A. O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev.
Lett.94(2005) 111601, arXiv:hep-th/0405231.
[34] J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. A.
Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618.
[35] H. Liu, K. Rajagopal, and U. A. Wiedemann, Calculating the jet quenching parameter from AdS/CFT, Phys. Rev. Lett.97(2006) 182301, arXiv:hep-ph/0605178.
[36] H. Liu, K. Rajagopal, and U. A. Wiedemann, Wilson loops in heavy ion collisions and their calculation in AdS/CFT, JHEP03(2007) 066, arXiv:hep-ph/0612168.
[37] C. P. Herzog, A. Karch, P. Kovtun, C. Kozcaz, and L. G. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP07(2006) 013, arXiv:hep-th/0605158.
[38] S. D. Avramis and K. Sfetsos, Supergravity and the jet quenching parameter in the presence of R-charge densities, JHEP01(2007) 065, arXiv:hep-th/0606190.
[39] S. S. Gubser, Drag force in AdS/CFT, Phys. Rev.D74(2006) 126005, arXiv:hep-th/0605182.
[40] S. B. Giddings and A. Nudelman, Gravitational collapse and its boundary description in AdS, JHEP02(2002) 003,
arXiv:hep-th/0112099.
[41] S. Lin and E. Shuryak, Toward the AdS/CFT Gravity Dual for High Energy Collisions. 3.Gravitationally Collapsing Shell and
Quasiequilibrium, Phys. Rev.D78(2008) 125018, arXiv:0808.0910.
[42] P. M. Chesler and L. G. Yaffe, Horizon formation and
far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett.102(2009) 211601, arXiv:0812.2053.
[43] P. M. Chesler and L. G. Yaffe, Boost invariant flow, black hole
formation, and far-from- equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory, Phys. Rev.D82(2010) 026006, arXiv:0906.4426.
[44] S. Bhattacharyya and S. Minwalla, Weak Field Black Hole Formation in Asymptotically AdS Spacetimes, JHEP09(2009) 034, arXiv:0904.0464.
[45] S. Sachdev, Quantum magnetism and criticality, Nature Physics4 (Mar., 2008) 173–185, arXiv:0711.3015.
[46] S. Sachdev, Where is the quantum critical point in the cuprate superconductors?, arXiv:0907.0008.
[47] S. Sachdev, Condensed matter and AdS/CFT, arXiv:1002.2947.
[48] M. Ammon, J. Erdmenger, V. Grass, P. Kerner, and A. O’Bannon, On Holographic p-wave Superfluids with Back-reaction, Phys. Lett.B686 (2010) 192–198, arXiv:0912.3515.
[49] Y. Shin, C. Schunck, A. Schirotzek, and W. Ketterle, Phase diagram of a two-component Fermi gas with resonant interactions, Nature451 (2008), no. 4, 689–693.
[50] L.-y. He, M. Jin, and P.-f. Zhuang, Pion superfluidity and meson properties at finite isospin density, Phys. Rev.D71(2005) 116001, arXiv:hep-ph/0503272.
[51] A. G. Green and S. L. Sondhi, Nonlinear Quantum Critical Transport and the Schwinger Mechanism for a Superfluid-Mott-Insulator
Transition of Bosons, Phys. Rev. Lett.95(Dec, 2005) 267001.
[52] A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP09(2007) 024, arXiv:0705.3870.
[53] A. O’Bannon, Hall Conductivity of Flavor Fields from AdS/CFT, Phys.
Rev.D76(2007) 086007, arXiv:0708.1994.
[54] A. Karch, A. O’Bannon, and E. Thompson, The Stress-Energy Tensor of Flavor Fields from AdS/CFT, arXiv:0812.3629.
[55] D. Grumiller and P. Romatschke, On the collision of two shock waves in AdS5, JHEP08(2008) 027, arXiv:0803.3226.
[56] J. L. Albacete, Y. V. Kovchegov, and A. Taliotis, Modeling Heavy Ion Collisions in AdS/CFT, JHEP07(2008) 100, arXiv:0805.2927.
[57] S. S. Gubser, S. S. Pufu, and A. Yarom, Entropy production in collisions of gravitational shock waves and of heavy ions, Phys. Rev.
D78(2008) 066014, arXiv:0805.1551.
[58] S. Lin and E. Shuryak, Grazing Collisions of Gravitational Shock Waves and Entropy Production in Heavy Ion Collision, Phys. Rev.D79 (2009) 124015, arXiv:0902.1508.
[59] Y. V. Kovchegov and S. Lin, Toward Thermalization in Heavy Ion Collisions at Strong Coupling, JHEP03(2010) 057, arXiv:0911.4707.
[60] I. Y. Aref’eva, A. A. Bagrov, and L. V. Joukovskaya, Critical Trapped Surfaces Formation in the Collision of Ultrarelativistic Charges in (A)dS, JHEP03(2010) 002, arXiv:0909.1294.
[61] I. Y. Aref’eva, A. A. Bagrov, and E. A. Guseva, Critical Formation of Trapped Surfaces in the Collision of Non-expanding Gravitational Shock Waves in de Sitter Space- Time, JHEP12(2009) 009, arXiv:0905.1087.
[62] S. Lin and E. Shuryak, On the critical condition in gravitational shock wave collision and heavy ion collisions, Phys. Rev.D83(2011) 045025, arXiv:1011.1918.
[63] A. Taliotis, Heavy Ion Collisions with Transverse Dynamics from Evolving AdS Geometries, JHEP09(2010) 102, arXiv:1004.3500.
[64] A. Taliotis, Evolving Geometries in General Relativity, arXiv:1007.1452.
[65] A. Duenas-Vidal and M. A. Vazquez-Mozo, Colliding AdS
gravitational shock waves in various dimensions and holography, JHEP 07(2010) 021, arXiv:1004.2609.
[66] P. M. Chesler and L. G. Yaffe, Holography and colliding gravitational shock waves in asymptotically AdS5 spacetime, Phys. Rev. Lett.106 (2011) 021601, arXiv:1011.3562.
[67] U. H. Danielsson, E. Keski-Vakkuri, and M. Kruczenski, Spherically collapsing matter in AdS, holography, and shellons, Nucl. Phys.B563 (1999) 279–292, arXiv:hep-th/9905227.
[68] U. H. Danielsson, E. Keski-Vakkuri, and M. Kruczenski, Black hole formation in AdS and thermalization on the boundary, JHEP02(2000) 039, arXiv:hep-th/9912209.
[69] I. Amado and C. Hoyos-Badajoz, AdS black holes as reflecting cavities, JHEP09(2008) 118, arXiv:0807.2337.
[70] J. Wess and J. Bagger,Supersymmetry and Supergravity. Princeton University Press, 2nd edition ed., 1992.
[71] J. Polchinski, Dirichlet-Branes and Ramond-Ramond Charges, Phys.
Rev. Lett.75(1995) 4724–4727, arXiv:hep-th/9510017.
[72] J. Polchinski, Lectures on D-branes, arXiv:hep-th/9611050.
[73] E. Witten, Bound states of strings and p-branes, Nucl. Phys.B460 (1996) 335–350, arXiv:hep-th/9510135.
[74] R. G. Leigh, Dirac-Born-Infeld Action from Dirichlet Sigma Model, Mod. Phys. Lett.A4(1989) 2767.
[75] E. Witten, Solutions of four-dimensional field theories via M- theory, Nucl. Phys.B500(1997) 3–42, arXiv:hep-th/9703166.
[76] C. V. Johnson,D-Branes. Cambridge University Press, 2003.
[77] G. T. Horowitz and A. Strominger, Black strings and p-branes, Nuclear Physics B360(1991) 197–209.
[78] N. Beisertet al., Review of AdS/CFT Integrability: An Overview, arXiv:1012.3982.
[79] T. Hooft, A planar diagram theory for strong interactions, Nuclear Physics B72(1974) 461–473.
[80] F. Rust, In-medium effects in the holographic quark-gluon plasma, Adv.
High Energy Phys.2010(2010) 564624, arXiv:1003.0187.
[81] D. T. Son and A. O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP09(2002) 042, arXiv:hep-th/0205051.
[82] J. M. Figueroa-O’Farrill, BUSSTEPP lectures on supersymmetry, arXiv:hep-th/0109172.
[83] N. Beisert, The dilatation operator of N = 4 super Yang-Mills theory and integrability, Phys. Rept.405(2005) 1–202, arXiv:hep-th/0407277.
[84] I. R. Klebanov, Testing the AdS/CFT Correspondence, AIP Conf. Proc.
1031(2008) 3–20.
[85] V. Balasubramanian and P. Kraus, Spacetime and the holographic renormalization group, Phys. Rev. Lett.83(1999) 3605–3608, arXiv:hep-th/9903190.
[86] P. Breitenlohner and D. Z. Freedman, Positive Energy in anti-De Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett.B115 (1982) 197.
[87] P. Breitenlohner and D. Z. Freedman, Stability in Gauged Extended Supergravity, Ann. Phys.144(1982) 249.
[88] P. K. Townsend, Positive energy and the scalar potential in higher dimensional (super)gravity theories, Phys. Lett.B148(1984) 55.
[89] S. Lee, S. Minwalla, M. Rangamani, and N. Seiberg, Three-point functions of chiral operators in D = 4, N = 4 SYM at large N, Adv.
Theor. Math. Phys.2(1998) 697–718, arXiv:hep-th/9806074.
[90] K. G. Wilson, Confinement of quarks, Phys. Rev. D10(Oct, 1974) 2445–2459.
[91] J. M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett.
80(1998) 4859–4862, arXiv:hep-th/9803002.
[92] S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J.C22(2001) 379–394, arXiv:hep-th/9803001.
[93] E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys.2(1998) 505–532, arXiv:hep-th/9803131.
[94] A. K. Das, Topics in finite temperature field theory, arXiv:hep-ph/0004125.
[95] S. M. Carroll,Spacetime and Geometry. Adison Wesley, 2004.
[96] S. W. Hawking and D. N. Page, Thermodynamics of Black Holes in anti-De Sitter Space, Commun. Math. Phys.87(1983) 577.
[97] V. E. Hubeny and M. Rangamani, A holographic view on physics out of equilibrium, Adv. High Energy Phys.2010(2010) 297916,
arXiv:1006.3675.
[98] S.-J. Rey, S. Theisen, and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large N gauge theory and anti-de Sitter supergravity, Nucl. Phys.B527(1998) 171–186, arXiv:hep-th/9803135.
[99] A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP06(2002) 043, arXiv:hep-th/0205236.
[100] J. Erdmenger, N. Evans, I. Kirsch, and E. Threlfall, Mesons in Gauge/Gravity Duals - A Review, Eur. Phys. J.A35(2008) 81–133, arXiv:0711.4467.
[101] M. Grana and J. Polchinski, Gauge / gravity duals with holomorphic dilaton, Phys. Rev.D65(2002) 126005, arXiv:hep-th/0106014.
[102] M. Bertolini, P. Di Vecchia, M. Frau, A. Lerda, and R. Marotta, N = 2 gauge theories on systems of fractional D3/D7 branes, Nucl. Phys.
B621(2002) 157–178, arXiv:hep-th/0107057.
[103] F. Bigazziet al., D3-D7 Quark-Gluon Plasmas, JHEP11(2009) 117, arXiv:0909.2865.
[104] F. Bigazzi, A. L. Cotrone, J. Mas, D. Mayerson, and J. Tarrio, D3-D7 Quark-Gluon Plasmas at Finite Baryon Density, JHEP04(2011) 060, arXiv:1101.3560.
[105] S. Kobayashi, D. Mateos, S. Matsuura, R. C. Myers, and R. M.
Thomson, Holographic phase transitions at finite baryon density, JHEP 02(2007) 016, arXiv:hep-th/0611099.
[106] K. Skenderis, Lecture notes on holographic renormalization, Class.
Quant. Grav.19(2002) 5849–5876, arXiv:hep-th/0209067.
[107] A. Karch, A. O’Bannon, and K. Skenderis, Holographic
renormalization of probe D-branes in AdS/CFT, JHEP04(2006) 015, arXiv:hep-th/0512125.
[108] J. Babington, J. Erdmenger, N. J. Evans, Z. Guralnik, and I. Kirsch, Chiral symmetry breaking and pions in non-supersymmetric gauge / gravity duals, Phys. Rev.D69(2004) 066007, arXiv:hep-th/0306018.
[109] V. G. Filev, C. V. Johnson, R. C. Rashkov, and K. S. Viswanathan, Flavoured large N gauge theory in an external magnetic field, JHEP10 (2007) 019, arXiv:hep-th/0701001.
[110] J. Erdmenger, R. Meyer, and J. P. Shock, AdS/CFT with Flavour in Electric and Magnetic Kalb-Ramond Fields, JHEP12(2007) 091, arXiv:0709.1551.
[111] J. Polchinski and M. J. Strassler, The string dual of a confining four-dimensional gauge theory, arXiv:hep-th/0003136.
[112] H. Liu, J. McGreevy, and D. Vegh, Non-Fermi liquids from holography, arXiv:0903.2477.
[113] J. D. Bekenstein, Black hole hair: Twenty-five years after, arXiv:gr-qc/9605059.
[114] S. S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev.D78(2008) 065034, arXiv:0801.2977.
[115] M. N. Chernodub and A. S. Nedelin, Phase diagram of chirally imbalanced QCD matter, arXiv:1102.0188.
[116] M. Tinkham,Introduction to Superconductivity. McGraw-Hill Kogakusha, Ltd., 1975.
[117] V. L. Ginzburg and L. D. Landau, On the Theory of superconductivity, Zh. Eksp. Teor. Fiz.20(1950) 1064–1082.
[118] K. Maeda and T. Okamura, Characteristic length of an AdS/CFT superconductor, Phys. Rev.D78(2008) 106006, arXiv:0809.3079.
[119] H.-B. Zeng, Z.-Y. Fan, and H.-S. Zong, Superconducting Coherence Length and Magnetic Penetration Depth of a p-wave Holographic Superconductor, Phys. Rev.D81(2010) 106001, arXiv:0912.4928.
[120] O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10(2008) 091, arXiv:0806.1218.
[121] R. C. Myers, Dielectric-branes, JHEP12(1999) 022, arXiv:hep-th/9910053.
[122] A. Karch and A. O’Bannon, Holographic Thermodynamics at Finite Baryon Density: Some Exact Results, JHEP11(2007) 074,
arXiv:0709.0570.
[123] J. Erdmenger, M. Kaminski, P. Kerner, and F. Rust, Finite baryon and isospin chemical potential in AdS/CFT with flavor, JHEP11(2008) 031, arXiv:0807.2663.
[124] A. O’Bannon, Toward a Holographic Model of Superconducting Fermions, JHEP01(2009) 074, arXiv:0811.0198.
[125] M. Ammon, J. Erdmenger, M. Kaminski, and A. O’Bannon, Fermionic Operator Mixing in Holographic p-wave Superfluids, JHEP05(2010) 053, arXiv:1003.1134.
[126] S. K. Rama, S. Sarkar, B. Sathiapalan, and N. Sircar, Strong Coupling BCS Superconductivity and Holography, arXiv:1104.2843.
[127] S. S. Gubser and S. S. Pufu, The gravity dual of a p-wave superconductor, JHEP11(2008) 033, arXiv:0805.2960.
[128] S. S. Gubser, Colorful horizons with charge in anti-de Sitter space, Phys. Rev. Lett.101(2008) 191601, arXiv:0803.3483.
[129] P. Basu, J. He, A. Mukherjee, and H.-H. Shieh, Hard-gapped Holographic Superconductors, Phys. Lett.B689(2010) 45–50, arXiv:0911.4999.
[130] R. Manvelyan, E. Radu, and D. H. Tchrakian, New AdS non Abelian black holes with superconducting horizons, Phys. Lett.B677(2009) 79–87, arXiv:0812.3531.
[131] V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys.208(1999) 413–428,
arXiv:hep-th/9902121.
[132] S. de Haro, S. N. Solodukhin, and K. Skenderis, Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence, Commun. Math. Phys.217(2001) 595–622, arXiv:hep-th/0002230.
[133] N. Iqbal, H. Liu, M. Mezei, and Q. Si, Quantum phase transitions in holographic models of magnetism and superconductors, Phys. Rev.D82 (2010) 045002, arXiv:1003.0010.
[134] D. B. Kaplan, J.-W. Lee, D. T. Son, and M. A. Stephanov, Conformality Lost, Phys. Rev.D80(2009) 125005, arXiv:0905.4752.
[135] G. T. Horowitz and M. M. Roberts, Zero Temperature Limit of
Holographic Superconductors, JHEP11(2009) 015, arXiv:0908.3677.
[136] C. P. Herzog and S. S. Pufu, The Second Sound of SU(2), JHEP04 (2009) 126, arXiv:0902.0409.
[137] C. P. Herzog, An Analytic Holographic Superconductor, Phys. Rev.
D81(2010) 126009, arXiv:1003.3278.
[138] P. Basu, J. He, A. Mukherjee, and H.-H. Shieh, Superconductivity from D3/D7: Holographic Pion Superfluid, JHEP11(2009) 070,
arXiv:0810.3970.
[139] P. Koerber and A. Sevrin, The non-abelian D-brane effective action through order alpha’**4, JHEP10(2002) 046, arXiv:hep-th/0208044.
[140] A. A. Tseytlin, On non-abelian generalisation of the Born-Infeld action in string theory, Nucl. Phys.B501(1997) 41–52,
arXiv:hep-th/9701125.
[141] A. Hashimoto and W. Taylor, Fluctuation spectra of tilted and intersecting D-branes from the Born-Infeld action, Nucl. Phys.B503 (1997) 193–219, arXiv:hep-th/9703217.
[142] N. R. Constable, R. C. Myers, and O. Tafjord, The noncommutative bion core, Phys. Rev.D61(2000) 106009, arXiv:hep-th/9911136.
[143] R. C. Myers and M. C. Wapler, Transport Properties of Holographic Defects, JHEP12(2008) 115, arXiv:0811.0480.
[144] D. Mateos, S. Matsuura, R. C. Myers, and R. M. Thomson,
Holographic phase transitions at finite chemical potential, JHEP11 (2007) 085, arXiv:0709.1225.
[145] D. Mateos, R. C. Myers, and R. M. Thomson, Thermodynamics of the brane, JHEP05(2007) 067, arXiv:hep-th/0701132.
[146] J. Erdmenger, M. Kaminski, and F. Rust, Holographic vector mesons from spectral functions at finite baryon or isospin density, Phys. Rev.
D77(2008) 046005, arXiv:0710.0334.
[147] A. Karch and S. L. Sondhi, Non-linear, Finite Frequency Quantum Critical Transport from AdS/CFT,. Comments: 16 pages.
[148] A. O’Bannon, Holographic Thermodynamics and Transport of Flavor Fields, arXiv:0808.1115.
[149] S. S. Gubser and A. Yarom, Linearized hydrodynamics from probe-sources in the gauge- string duality, arXiv:0803.0081.
[150] C. P. Herzog, P. Kovtun, S. Sachdev, and D. T. Son, Quantum critical transport, duality, and M-theory, Phys. Rev.D75(2007) 085020, arXiv:hep-th/0701036.
[151] S. A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev.D76(2007) 066001, arXiv:0704.1160.
[152] S. A. Hartnoll, P. K. Kovtun, M. Muller, and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes, Phys. Rev.B76(2007) 144502, arXiv:0706.3215.
[153] S. A. Hartnoll and C. P. Herzog, Ohm’s Law at strong coupling: S duality and the cyclotron resonance, Phys. Rev.D76(2007) 106012, arXiv:0706.3228.
[154] J. Erdmenger, M. Haack, M. Kaminski, and A. Yarom, Fluid dynamics of R-charged black holes, JHEP01(2009) 055, arXiv:0809.2488.
[155] N. Banerjeeet al., Hydrodynamics from charged black branes, JHEP01 (2011) 094, arXiv:0809.2596.
[156] D. T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett.103(2009) 191601, arXiv:0906.5044.
[157] A. Karch and A. O’Bannon, Chiral transition of N = 4 super
Yang-Mills with flavor on a 3-sphere, Phys. Rev.D74(2006) 085033, arXiv:hep-th/0605120.
[158] I. Kirsch, Generalizations of the AdS/CFT correspondence, Fortsch.
Phys.52(2004) 727–826, arXiv:hep-th/0406274.
[159] K. Ghoroku, T. Sakaguchi, N. Uekusa, and M. Yahiro, Flavor quark at high temperature from a holographic model, Phys. Rev.D71(2005) 106002, arXiv:hep-th/0502088.
[160] D. Mateos, R. C. Myers, and R. M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett.97(2006) 091601, arXiv:hep-th/0605046.
[161] T. Albash, V. G. Filev, C. V. Johnson, and A. Kundu, A
topology-changing phase transition and the dynamics of flavour, Phys.
Rev.D77(2008) 066004, arXiv:hep-th/0605088.
[162] C. Hoyos-Badajoz, K. Landsteiner, and S. Montero, Holographic Meson Melting, JHEP04(2007) 031, arXiv:hep-th/0612169.
[163] T. Albash, V. G. Filev, C. V. Johnson, and A. Kundu, Finite Temperature Large N Gauge Theory with Quarks in an External Magnetic Field, JHEP07(2008) 080, arXiv:0709.1547.
[164] A. O’Bannon, Toward a Holographic Model of Superconducting Fermions, JHEP01(2009) 074, arXiv:0811.0198.
[165] R. M. Wald, General Relativity,. Chicago, Usa: Univ. Pr. (1984) 491p.
[166] R. A. Janik and R. B. Peschanski, Asymptotic perfect fluid dynamics as a consequence of AdS/CFT, Phys. Rev.D73(2006) 045013,
arXiv:hep-th/0512162.
[167] M. P. Heller and R. A. Janik, Viscous hydrodynamics relaxation time from AdS/CFT, Phys. Rev.D76(2007) 025027, arXiv:hep-th/0703243.
[168] J. Abajo-Arrastia, J. Aparicio, and E. Lopez, Holographic Evolution of Entanglement Entropy, JHEP11(2010) 149, arXiv:1006.4090.
[169] T. Albash and C. V. Johnson, Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches, New J. Phys.13 (2011) 045017, arXiv:1008.3027.
[170] V. Balasubramanianet al., Thermalization of Strongly Coupled Field Theories, arXiv:1012.4753.
[171] V. E. Hubeny, H. Liu, and M. Rangamani, Bulk-cone singularities and signatures of horizon formation in AdS/CFT, JHEP01(2007) 009, arXiv:hep-th/0610041.
[172] D. Z. Freedman, S. D. Mathur, A. Matusis, and L. Rastelli, Correlation functions in the CFT(d)/AdS(d+ 1) correspondence, Nucl. Phys.B546 (1999) 96–118, arXiv:hep-th/9804058.
[173] K.-c. Chou, Z.-b. Su, B.-l. Hao, and L. Yu, Equilibrium and
Nonequilibrium Formalisms Made Unified, Phys. Rept.118(1985) 1.
[174] N. P. Landsman and C. G. van Weert, Real and Imaginary Time Field Theory at Finite Temperature and Density, Phys. Rept.145(1987) 141.
[175] K. Skenderis and B. C. van Rees, Real-time gauge/gravity duality, Phys. Rev. Lett.101(2008) 081601, arXiv:0805.0150.
[176] K. Skenderis and B. C. van Rees, Real-time gauge/gravity duality:
Prescription, Renormalization and Examples, JHEP05(2009) 085, arXiv:0812.2909.
[177] B. C. van Rees, Real-time gauge/gravity duality and ingoing boundary conditions, Nucl. Phys. Proc. Suppl.192-193(2009) 193–196,
arXiv:0902.4010.
[178] F. G. Tricomi,Integral equations. Dover, New York, USA, 1985.
[179] T. Banks, M. R. Douglas, G. T. Horowitz, and E. J. Martinec, AdS dynamics from conformal field theory, arXiv:hep-th/9808016.
[180] V. Balasubramanian and S. F. Ross, Holographic particle detection, Phys. Rev.D61(2000) 044007, arXiv:hep-th/9906226.
[181] R. A. Janik and R. B. Peschanski, Gauge / gravity duality and
thermalization of a boost- invariant perfect fluid, Phys. Rev.D74(2006) 046007, arXiv:hep-th/0606149.
[182] W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim.B44S10(1966) 1.
[183] W. Zhuxi and G. Dunren,An introduction to special functions. Chinese Scientific, Beijing China, 2000.
[184] I. S. Gradshteyn and I. M. Ryzhik,Tables of integrals, series and products. Academic Press, Boston, USA, 7 ed., 2007.
[185] E. Barnes, D. Vaman, C. Wu, and P. Arnold, Real-time
finite-temperature correlators from AdS/CFT, Phys. Rev.D82(2010) 025019, arXiv:1004.1179.