Temperature dependence of η/s in the “s”-QGP “s”-QGP: transition region near T d ; d=deconfinement. Here: “s” semi, not strong. Matrix model for semi-QGP in moderate coupling. Without quarks (just glue): transition region narrow, T c → ~ 1.2 T c. With quarks: T χ ≠ “T d ”: χ = chiral. Transition region broad. Today: temperature dependence of η/s in matrix model. RDP & Skokov, Kashiwa, RDP, & Skokov, Dumitru, Guo, Hidaka, Korthals-Altes, & RDP, & RDP & Hidaka, , , , ; RDP, ph/ Dumitru, Lenaghan, & RDP, ph/ Dumitru, Hatta, Lenaghan, Orginos, & RDP, th/ Meisinger, Miller, & Ogilvie, ph/ ; RDP, arXiv:hep-ph/

Quasi-particle picture of deconfined gluons: weird ⇐ Borsanyi, Endrodi, Fodor, Katz, & Szabo, t = T/T d → “Pure” SU(3), no quarks. Pressure very small below T d. m gluon (t)↑ T/T d → Castorina, Miller, Satz ⇒ Fit p(T) with massive gluon quasi-particles T >1. 2 T d : m gluon ~ T. “Perturbative”, m~gT T: T d →1.2 T d : to suppress pressure, huge increase in m gluon (T). Weird.

Lattice: it’s not a bag constant Lattice: T: T d → 1.2 T d - complicated T: 1.2 T d → 4 T d : simplicity! 10 T d ↑ ↑ T d Borsanyi, Endrodi, Fodor, ⇒ Katz, & Szabo, For T: 1.2 T d → 4 T d : Above 1.2 T d, the leading corrections to ideality are not a MIT bag constant, but ~ T 2

Order parameter for deconfinement Thermal Wilson line: Trace = Polyakov loop, gauge invariant L gauge dependent, eigenvalues gauge invariant: eigenvalues basic variables of matrix model 〈 loop 〉 measures ionization of color: 〈 loop 〉 = 1 ⇒ complete ionization; perturbative regime 〈 loop 〉 = 0 ⇒ no ionization; confined phase 0 < 〈 loop 〉 < 1, partial ionization, “semi”-QGP Td↑Td↑ T→ ↑

Loops from the lattice Bazavov & Petreczky, ⇒ At same T, quarks act to increase : SU(3), with quarks↓ ⇐ SU(2), no quarks ⇐ SU(3), no quarks T→ ↑ ↓T d SU(2) T d SU(3) ↓ T χ QCD ↑

Only glue: matrix model for deconfinement Simplest possible approximation: constant A 0 Necessary to model change in 〈 loop 〉 Effective potential: perturbative term, ~T 4, + non-perturbative term ~ T d 2 T 2, added by hand Typical mean field potential: For T: T d → 1.2 T d : 〈 q 〉 ≠ 0, details of V eff (q) matter. But for T > 1.2 T d - 〈 q 〉 ~ 0, V non (q) = constant ≠ 0, so:

Only glue: pressure With two free parameters, fit to pressure(T): Lattice: Beinlich, Peikert, & Karsch lat/ ; Datta & Gupta ↑ T d 3T d ↑ T→ ⇐ Lattice ⇐ 2-parameter

Only glue: ‘t Hooft loop With no adjustment, fit to second function of T, ‘t Hooft loop Semi-classical: Giovannangeli & Korthals-Altes, GKA: ph/ , ph/ Lattice: de Forcrand, D’Elia, Pepe, lat/ ; de Forcrand, Noth lat/ Semi-classical, GKA ⇓ ⇐ N = 2 ⇐ matrix model, N = 3 T→ lattice, N=3 ⇓ 5 T c ↑↑ T c

Only glue: Polyakov loop? Polyakov loop in matrix model ≠ (renormalized) loop from lattice Does the renormalized Polyakov loop reflect the eigenvalues of L? ⇐ lattice ⇑ 0-parameter 1-parameter ⇓ Lattice: Gupta, Hubner, and Kaczmarek, ↑ T c 1.5 T c ↑T→ ⇐ 2 parameter

Matrix model with heavy quarks Add heavy quarks perturbatively, change nothing else. Compute position of Deconfining Critical Endpoint, DCE. Matrix model: m DCE ~ 2.4 GeV, T DCE ~ 0.99 T d. Lattice: m DCE ~ 2.25 GeV, T DCE ~ 0.99 T d. Fromm, Langelage, Lottini, & Philipsen, Kashiwa, RDP, ⇒ & Skokov,

From here on: Matrix model for SU(N c ) gluons Two cases: only glue, and with N f flavors of massless quarks N c = N f = ∞

Loops In matrix model, no strong relation between T χ and T d ! T→ ↑ Td↑Td↑ with quarks ⇒ ⇐ only glue Tχ↑Tχ↑

Effective gluon masses T→ Td↑Td↑ with quarks ⇑ ⇐ only glue Tχ↑Tχ↑ Define effective gluon mass from loop: Like “weird” quasi-particle models! m gluon ↑

Other loops ⇐ only glue with quarks ⇒ Tχ↑Tχ↑ Td↑Td↑ T→ Many loops. E.g.: Not necessarily positive, so no m eff

Interaction measure with quarks ⇒ only glue ⇒ Tχ↑Tχ↑ ↑T d T→ e = energy density p = pressure

Entropy with quarks ⇒ only glue ⇓ Tχ↑Tχ↑ ↑T d T→ s = entropy density

Shear viscosity/entropy ↑T d Tχ↑Tχ↑ with quarks ⇒ only glue ⇓ T→ Shear viscosity η ~ ρ 2 /σ, ρ = density, σ = cross section. sQGP: σ ~ 〈 loop 〉 2, but: ρ ~ 〈 loop 〉 2, so η ~ 〈 loop 〉 2, suppressed for small 〈 loop 〉

Conclusions Temperature dependence of η/s very sensitive to 〈 loop 〉 Ordinary kinetic theory: small η only for large coupling. Semi-QGP non-standard kinetic theory: Even though σ small, so is η, because of small density ρ Density of color charges ρ must become small in a partially ionized phase Energy loss: dE/dx ~ coupling ~ large in ordinary kinetic theory dE/dx ~ small in semi-QGP Matrix model: effective theory, based upon lattice simulations. Competition for AdS/CFT.

Related work (“Weird”) quasi-particle models: Peshier, Kampfer, Pavlenko, Soff ’96, Peshier, ph/ ; Peshier & Cassing, ph/ ; Cassing, & Parton Hadron String Dynamics: Cassing & Bratkovskaya, Bratkovskaya, Cassing, Konchakovski, & Linnyk, Present model non-linear; linear matrix models: Vuorinen & Yaffe, ph/ ; de Forcrand, Kurkela, & Vuorinen, ; Zhang, Brauer, Kurkela, & Vuorinen, Narrow transition region: Braun, Gies, Pawlowski, ; Marhauser & Pawlowski, ; Braun, Eichhorn, Gies, & Pawlowski, Deriving effective theory from QCD: Monopoles: Liao & Shuryak, , ; Shuryak & Sulejmanpasic, 2012 Dyons: Diakonov & Petrov, Bions: Unsal Poppitz, Schaefer, & Unsal Standard kinetic theory and η, dE/dx: Majumder, Muller, & Wang, ph/ ; Liao & Shuryak, Asakawa, Bass, & Muller, ph/ , ph/ Center domains: Asakawa, Bass, & Muller,