Example charge diffusion ficks law 1855 conservation

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Need to add constitutive relations! Example: charge diffusion [Fick’s law (1855)] Conservation law Constitutive relation Diffusion equation Dispersion relation Expansion parameters:
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M,J,Q Holographically dual system in thermal equilibrium M, J, Q T S Gravitational fluctuations Deviations from equilibrium ???? and B.C. Quasinormal spectrum 10-dim gravity 4-dim gauge theory – large N, strong coupling
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From brane dynamics to AdS/CFT correspondence Open strings picture: dynamics of coincident D3 branes at low energy is described by Closed strings picture: dynamics of coincident D3 branes at low energy is described by conjectured exact equivalence Maldacena (1997); Gubser, Klebanov, Polyakov (1998); Witten (1998)
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AdS/CFT correspondence conjectured exact equivalence Generating functional for correlation functions of gauge-invariant operators String partition function In particular Classical gravity action serves as a generating functional for the gauge theory correlators Latest test: Janik’08
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4D boundary z 0 The bulk and the boundary in AdS/CFT correspondence 5D bulk (+5 internal dimensions) UV/IR: the AdS metric is invariant under z plays a role of inverse energy scale in 4D theory
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supersymmetric Yang-Mills is the harmonic oscillator of the XXI century!
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Field content: Action: Gliozzi,Scherk,Olive’77 Brink,Schwarz,Scherk’77 (super)conformal field theory = coupling doesn’t run supersymmetric YM theory
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AdS/CFT correspondence is the simplest example of the gauge/string (gauge/gravity) duality
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Computing transport coefficients from “first principles” Kubo formulae allows one to calculate transport coefficients from microscopic models In the regime described by a gravity dual the correlator can be computed using the gauge theory/gravity duality Fluctuation-dissipation theory (Callen, Welton, Green, Kubo)
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Computing transport coefficients from dual gravity Assuming validity of the gauge/gravity duality, all transport coefficients are completely determined by the lowest frequencies in quasinormal spectra of the dual gravitational background This determines kinetics in the regime of a thermal theory where the dual gravity description is applicable (D.Son, A.S., hep-th/0205051, P.Kovtun, A.S., hep-th/0506184) Transport coefficients and quasiparticle spectra can also be obtained from thermal spectral functions
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First-order transport coefficients in N = 4 SYM in the limit Shear viscosity Bulk viscosity Charge diffusion constant Supercharge diffusion constant Thermal conductivity Electrical conductivity (G.Policastro, 2008) for non-conformal theories see Buchel et al; G.D.Moore et al Gubser et al.
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