Prof. Peter Mustermann I Institute of xxxxx I www.hzdr.deMember of the Helmholtz Associationpage 1

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

Equation of State and Viscosities from a Gravity Dual (AdS/QCD)

B. Kämpfer

Helmholtz-Zentrum Dresden-Rossendorf Technische Universität Dresden

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 2

water:

viscosity is importantfor flow pattern and splashes

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 3

Bulk Viscosity Could Matter

Dusling, Schafer, PRC 85 (2012) 044909

pQCD (leading log):

48

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 4

Bulk Viscosity Matters

Noronha-Hostler, Denicol, Noronha, Andrade, Grassi arXiv:1305.1981

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 5

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

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 6

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

Compilation of Lattice Results & QPM

(1) EoS

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 7

a = 3.78, b = - 0.3

(2) relaxation time

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 8

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

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 9

gravity setup

metric ansatz (Riemann)

Einstein - Hilbert

gauged radial coordinate scale

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

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 10

U = V / (3 V‘)

EoS

0

AdSBekenstein

Hawking

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 11

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

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 12

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

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 13

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

different formulation:Eling, Oz, JHEP 1106 (2011) 007cf. Buchel, Gursoy, Kiritsis, JHEP 1109 (2011) 095

0

AdS

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 14

benefit: w/o further input spectral functions transport coefficients

as in QPM (Bluhm et al.)

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 15

bulk viscosity is not universal (as, e.g. shear viscosity/entropy) sensitive dependence on pot. parameters

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 16

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

including quarks: what is the right EoS?

if would be the same same V

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 17

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

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 18

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

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 19

Summary

after precise adjustment of EoS at lattice data

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 20

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

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Bluhm, BK, Redlich, PLB 709 (2012) 77 PRC 84 (2011) 025201 NPA 830 (2009) 737

Retro: Common Work with K. Redlich

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

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B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 23

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