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Holograpic Transport Coeffients Equation of State and Viscosities *)

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Holograpic Transport Coeffients

Equation of State and Viscosities *)

(AdS/QCD)

R. Yaresko, B. Kämpfer

Helmholtz-Zentrum Dresden-Rossendorf

and

Technische Universität Dresden

*) 1403.3581, 1306.0214

Mocsy, Sorensen

1008.3381

HYDRO:

EoS +

viscosities

, PHENIX, ALICE…

Big Bang

Inflation CMB COBE, WMAP, Planck

BICEP2

Noronha-Hostler, Denicol, Noronha, Andrade, Grassi, Phys.Rev. C88 (2013) 044916

Basar, Kharzeev, Skokov, PRL 109 (2012) 202303

Tuchin, arXiv:1301.0099

coupling of conformal anomaly to photons

solution of photon-v2 puzzle?

data: PHENIX

PRL 109 (2012) 122302

a = 3.78, b = - 0.3

physics in D + N D

quantum gravity QFT

e.g. AdS/CFT:

1997:

Maldacena,

Gubser et al.

Witten

isometries symmetry

classical gravity strongly coupled QFT

`t Hooft coupling

and Nc large

r infty: boundary

boundary

: holographic coordinate

(renorm.) scale

Z 1/r

blackness funct.

(simple zero horizon)

gravity dual of QCD is unknown

recipe: breaking of conf. symmetry duality with non-conf. QFT

bottom-up appr.: mimicing thermal QCD features/expectations

by 1 scalar („dilaton“)

kinetic term + potential

+ by 1 gauge field

T

n

Einstein - Hilbert

metric ansatz (Riemann)

gauged radial coordinate scale

Gubser et al. PRL 101 (2008) 131601, PRD 78 (2008) 086007

Kiritsis et al.: - 2 scalar eqs. for X‘, Y‘

- 2 quadratures LT, G_5 s

UV IR

Kiritsis et al.:

p(Tc) = 0

G_5 s

LT

LTc

phi_H

engineering the potential: EoS V

open questions: - a unique (master) V

- V vs. phase transition

bottom-up approach: EoS (lattice QCD) dilaton potential

exp. functs. from supergravity pots.

ansatz: Gubser type pot.

+ polynom. distortions

T/Tc vs. TL:

from T(s/T^3)

min. or turning

G5: from s/T^3

lattice QCD, SU(3) gauge theory, Borsanyi et al., JHEP 1207 (2012) 056

consistent with Boyd et al., NPB 469 (1996) 419

Gubser et al., JHEP 0808 (2008) 085

-2

Eling, Oz, JHEP 1106 (2011) 007

cf. Buchel et al., JHEP 1109 (2011) 095

= (d log s / d log phi_H)

AdS

0

shear viscosity is independent of V

KSS, JHEP 0310 (2003) 064

Policastro, Son, Starinets, PRL 87 (2001) 081601

bulk viscosity is not universal (as, e.g. shear viscosity/entropy)

sensitive dependence on pot. parameters

boundary (UV)

Tc

10 Tc

nearly the same EoS & bulk viscosity

also for Kititsis pot. (boundary at phi infty)

DeWolfe , Gubser, Rosen, Phys.Rev. D84 (2011) 126014, 83 (2011) 086005

models with CEP

spectral functions & medium on equal footing

beyond soft-wall models

temperature dependence of eta/s

beyond Einstein-Hilbert action

mu > 0 CEP:

Cremonini, Gursoy, Szepietowski,

JHEP 08 (2012) 167

DeWolfe, Gubser, Rosen, PRD 83 (2011) 086005,

PRD 84 (2011) 126014

and all the other transport coefficients

Abelian field strength of V

soft-wall model:

AdS/QCD, soft-wall model,

Cui. Takeuchi, Wu, 1112.5923

(T in GeV)

mass shift

JHEP 1204 (2012) 144

Schwarzschild BH Reissner-Nordstrom BH: chem. pot.

AdS/QCD, soft-wall model, Colangelo, Giannuzzi, Nicotri, 1201.1564, JHEP 1205 (2012) 076

mass shift + broadening

vision: beyond soft-wall ansatz dilaton consistent with EoS

problem: missing unique QCD results with quarks

5D Riemann: x,z 4D Minkowski: x

semi-class. gravity strongly coupled gauge theo.

X(x, z) gauge-inv. Operators (x)

asymp. AdS

black brane: T (Hawking)

s (Bekenstein)

semi-class. functional correlation functions

breaking conf. sym. by

mass scale, e.g. dilation

+ potential

Baier,Stricker, Taanila, Vuorinen, Phys.Rev. D86 (2012) 081901, JHEP 1207 (2012) 094

at T > 200 MeV, one obtains the thermalization time scale ~ 0.1 fm/c, which one might compare with the typical production time of dileptons with mass/energy larger than 5 GeV, tau_p < 0.04 fm/c. It appears that dilepton pairs produced early on have a reasonable chance to escape the system while it is still out of thermal equilibrium.

problem of particle production in dynamical systems

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