Holograpic Transport Coeffients Equation of State and Viscosities *)

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 1

B. Kampfer I Institute of Radiation Physics I www.hzdr.de

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


Big Bang

Inflation CMB COBE, WMAP, Planck BICEP2

, PHENIX, ALICE…

fromMocsy, Sorensen1008.3381

HYDRO:EoS +viscosities


water:

viscosity is importantfor flow pattern and splashes


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

coupling of conformal anomaly to photons

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

solution of photon-v2 puzzle?

data: PHENIXPRL 109 (2012) 122302

Tuchin, arXiv:1301.0099


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

bulk viscosity


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

Compilation of Lattice Results & QPM

(1) EoS


a = 3.78, b = - 0.3

(2) relaxation time


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


boundary

blackness funct. (simple zero horizon)

r = const: Minkowski slicesr infty: boundary

: holographic coordinate (renorm.) scale Z 1/r


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

metric ansatz (Riemann)

Einstein - Hilbert

gauged radial coordinate scale

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


U = V / (3 V‘)

EoS s(T)

0

AdSBekenstein

Hawking


Kiritsis et al.: - 2 scalar eqs. for X‘, Y‘ - 2 quadratures LT, G_5 s

phi_H

UV IR

G_5

s

LTLTc

Kiritsis et al.:p(Tc) = 0

open questions: - a unique (master) V - V vs. phase transition

engineering the potential: EoS V


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

ansatz: Gubser type pot. + polynom. distortions

T/Tc vs. TL:from T(s/T^3)min. or turning

G5: from s/T^3

exp. functs. from supergravity pots.


lattice QCD, SU(3) gauge theory, Borsanyi et al., JHEP 1207 (2012) 056 consistent with Boyd et al., NPB 469 (1996) 419


bulk viscosity

shear viscosity is independent of V

Gubser et al., JHEP 0808 (2008) 085

KSS, JHEP 0310 (2003) 064

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

Eling, Oz, JHEP 1106 (2011) 007cf. Buchel et al., JHEP 1109 (2011) 095

0

AdS

= (d log s / d log phi_H)-2


benefit: w/o further input 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

Tc from p = 0, beta function, confinement

J. Knaute (2014)


Is the Potential Unique?

10 Tc Tcboundary (UV)

nearly the same EoS & bulk viscosity

also for Kititsis pot. (boundary at phi infty)


including quarks

WB Collab.Phys.Lett. B730 (2014) 99

A. Bazavov [hotQCD], talk at QM2014, Tuesday


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

two dilaton „potentials“:

models with CEP


Summary

after precise adjustment of EoS at lattice data here: SU(3) YM


Outlook

spectral functions & medium on equal footing beyond soft-wall models

temperature dependence of eta/s beyond Einstein-Hilbert action

mu > 0 CEP: DeWolfe, Gubser, Rosen, PRD 83 (2011) 086005, PRD 84 (2011) 126014

Cremonini, Gursoy, Szepietowski, JHEP 08 (2012) 167

and all the other transport coefficients


AdS/QCD, soft-wall model, Cui. Takeuchi, Wu, 1112.5923

(T in GeV)

JHEP 1204 (2012) 144

meson in vector channel

Abelian field strength of Vsoft-wall model:

mass shift


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

Schwarzschild BH Reissner-Nordstrom BH: chem. pot.

vision: beyond soft-wall ansatz dilaton consistent with EoSproblem: missing unique QCD results with quarks

mass shift + broadening


AdS/QCD

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

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


with lin. fluct.

quark-mesonmodel

mfa

F. Wunderlich


lin. fluct.

50 MeVphotons

isentropes

lin. fluct.

Holograpic Transport Coeffients Equation of State and Viscosities *)

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