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Equation of State and Viscosities from a Gravity Dual (AdS/QCD). B. Kämpfer. Helmholtz-Zentrum Dresden-Rossendorf Technische Universität Dresden. viscosity is important for flow pattern and splashes. water:. Bulk Viscosity Could Matter. Dusling, Schafer, PRC 85 (2012) 044909.

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Equation of state and viscosities from a gravity dual ads qcd

Equation of State and Viscosities

from a Gravity Dual (AdS/QCD)

B. Kämpfer

Helmholtz-Zentrum Dresden-Rossendorf

Technische Universität Dresden


Equation of state and viscosities from a gravity dual ads qcd

viscosity is important

for flow pattern and splashes

water:


Equation of state and viscosities from a gravity dual ads qcd

Bulk Viscosity Could Matter

Dusling, Schafer, PRC 85 (2012) 044909

pQCD (leading log):

48


Equation of state and viscosities from a gravity dual ads qcd

Bulk Viscosity Matters

Noronha-Hostler, Denicol, Noronha, Andrade, GrassiarXiv:1305.1981


Equation of state and viscosities from a gravity dual ads qcd

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


Equation of state and viscosities from a gravity dual ads qcd

Compilation of Lattice Results & QPM

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

(1) EoS


Equation of state and viscosities from a gravity dual ads qcd

(2) relaxation time

a = 3.78, b = - 0.3


Equation of state and viscosities from a gravity dual ads qcd

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


Equation of state and viscosities from a gravity dual ads qcd

gravity setup

Einstein - Hilbert

metric ansatz (Riemann)

gauged radial coordinate  scale

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


Equation of state and viscosities from a gravity dual ads qcd

AdS

0

U = V / (3 V‘)

Bekenstein

Hawking

 EoS


Equation of state and viscosities from a gravity dual ads qcd

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


Equation of state and viscosities from a gravity dual ads qcd

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

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


Equation of state and viscosities from a gravity dual ads qcd

bulk viscosity (2012) 056

Gubser et al., JHEP 0808 (2008) 085

different formulation:

Eling, Oz, JHEP 1106 (2011) 007

cf. Buchel, Gursoy, Kiritsis, JHEP 1109 (2011) 095

AdS

0

shear viscosity is independent of V

KSS, JHEP 0310 (2003) 064

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


Equation of state and viscosities from a gravity dual ads qcd

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

 transport coefficients

as in QPM (Bluhm et al.)


Equation of state and viscosities from a gravity dual ads qcd

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

 sensitive dependence on pot. parameters


Equation of state and viscosities from a gravity dual ads qcd

including quarks: what is the right EoS? viscosity/entropy)

R.R. Caldwell, S.S. Gubser, DOI: 10.1103/PhysRevD.87.063523

Bazavov et al., PRD 80 (2009) 014504

Borsanyi et al., JHEP 1011 (2010) 077

u,d,s,g

if

would be the same  same V


Equation of state and viscosities from a gravity dual ads qcd

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


Equation of state and viscosities from a gravity dual ads qcd

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


Equation of state and viscosities from a gravity dual ads qcd

Summary viscosity/entropy)

after precise adjustment of EoS at lattice data


Equation of state and viscosities from a gravity dual ads qcd

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


Equation of state and viscosities from a gravity dual ads qcd

Retro: Common Work with K. Redlich viscosity/entropy)

Hentschel, BK, Pavlenko, Redlich, Soff, Z. Phys. C75 (1997) 333

Bluhm, BK, Redlich, PLB 709 (2012) 77

PRC 84 (2011) 025201

NPA 830 (2009) 737


Equation of state and viscosities from a gravity dual ads qcd

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