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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. from Mocsy, Sorensen

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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


from

Mocsy, Sorensen

1008.3381

HYDRO:

EoS +

viscosities

, PHENIX, ALICE…

Big Bang

Inflation CMB COBE, WMAP, Planck

BICEP2


viscosity is important

for flow pattern and splashes

water:


Bulk Viscosity Could Matter

Dusling, Schafer, PRC 85 (2012) 044909

pQCD (leading log):

48


Bulk Viscosity Matters

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


Bulk Viscosity Can Matter

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


bulk viscosity

orig.

Huovinen, Int.J.Mod.Phys. E22 (2013) 1330029


Compilation of Lattice Results & QPM

Bluhm et al., PLB 709 (2012) 77, PRC 84 (2011) 025201

(1) EoS


(2) relaxation time

a = 3.78, b = - 0.3


Holography

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 = const: Minkowski slices

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


gravity setup

Einstein - Hilbert

metric ansatz (Riemann)

gauged radial coordinate  scale

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


AdS

0

U = V / (3 V‘)

Bekenstein

Hawking

 EoS s(T)


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


bulk viscosity (2012) 056

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


benefit: w/o further input (2012) 056 spectral functions

 transport coefficients

as in QPM (Bluhm et al.)


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

 sensitive dependence on pot. parameters


Kiritsis et al. Model viscosity/entropy)

Tc from p = 0, beta function, confinement

J. Knaute (2014)


Is the Potential Unique? viscosity/entropy)

boundary (UV)

Tc

10 Tc

 nearly the same EoS & bulk viscosity

also for Kititsis pot. (boundary at phi  infty)


including quarks viscosity/entropy)

WB Collab.

Phys.Lett. B730 (2014) 99

A. Bazavov [hotQCD],

talk at QM2014, Tuesday


two dilaton „potentials“: viscosity/entropy)

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

models with CEP


Summary viscosity/entropy)

after precise adjustment of EoS at lattice data

here: SU(3) YM


Outlook viscosity/entropy)

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


meson in vector channel viscosity/entropy)

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 viscosity/entropy) 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


AdS/QCD viscosity/entropy)

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


AdS/CFT Emissivities viscosity/entropy)

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


F. Wunderlich viscosity/entropy)

quark-meson

model

mfa

with lin. fluct.


isentropes viscosity/entropy)

lin. fluct.

50 MeV

photons

lin. fluct.


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