The Big Picture. Thomas Schaefer. North Carolina State University

Transcription

1 The Big Picture Thomas Schaefer North Carolina State University 1

2 Big Questions What is QCD? What is a Phase of QCD? What is a Plasma? What is a (perfect) Liquid? What is a wqgp/sqgp? 2

3 What is QCD (Quantum Chromo Dynamics)? Elementary fields: Quarks Gluons color a = 1,..., 3 (q α ) a f spin α = 1, 2 A a color a = 1,..., 8 µ spin ɛ ± µ flavor f = u, d, s, c, b, t Dynamics: Generalized Maxwell (Yang-Mills) + Dirac theory L = q f (id/ m f )q f 1 4 Ga µνg a µν G a µν = µ A a ν ν A a µ + gf abc A b µa c ν id/ q = γ µ ( i µ + ga a µt a) q 3

4 Seeing Quarks and Gluons ALEPH DALI Run=15768 Evt=5906 Run=9063 Evt=7848 e + q e + q g Made on 28-Aug :39:06 by DREVERMANN with DALI_D7. Filename: DC015768_005906_960828_1338.PS_2J_3J e q e q 4

5 Asymptotic Freedom Classical field A cl µ. Modification due to quantum fluctuations: ( ( )) A µ = A cl 1 1 k µ + δa µ g 2 F cl 2 2 g 2 + c log µ 2 F 2 cl A cl µ (k) δa µ (p) δa µ δφ A cl ν (k) (2p + k) µ k ν F µν (2p + k) µ dielectric ɛ > 1 paramagnetic µ > 1 dielectric ɛ > 1 µɛ = 1 ɛ < 1 β(g) = g log(µ) = {[ g3 1 ] (4π) N c + 2 } 3 N f < 0 5

6 Running Coupling Constant 6

7 What is a Phase of QCD? Phases of Gauge Theories Coulomb Higgs Confinement V (r) e2 r V (r) e mr r V (r) kr Standard Model: U(1) SU(2) SU(3) 7

8 What is a Phase of QCD? Phases of Gauge Theories Coulomb Higgs Confinement V (r) e2 r V (r) e mr r V (r) kr QCD: High T phase High µ phase Low T, µ phase 8

9 Phases of Matter: Symmetries phase order broken rigidity Goldstone param symmetry phenomenon boson crystal ρ k translations rigid phonon magnet M rotations hysteresis magnon superfluid Φ particle number supercurrent phonon supercond. ψψ gauge symmetry supercurrent none (Higgs) χsb ψψ chiral symmetry axial current pion 9

10 Define left and right handed fields ψ L,R = 1 2 (1 ± γ 5)ψ Chiral Symmetry L R Fermionic lagrangian, M = diag(m u, m d, m s ) L = ψ L (id/ )ψ L + ψ R (id/ )ψ R L L R R + ψ L Mψ R + ψ R Mψ L L R R L M M M = 0: Chiral symmetry (L, R) SU(3) L SU(3) R ψ L Lψ L, ψ R Rψ R 10

11 Chiral Symmetry Breaking Chiral symmetry is spontaneously broken ψ f L ψg R + ψ f L ψg R (230 MeV)3 δ fg SU(3) L SU(3) R SU(3) V (G H) Consequences: dynamical mass generation m Q = 300 MeV m q m N = 890 MeV + 45 MeV (QCD, 95%) + (Higgs, 5%) Goldstone Bosons: Consider broken generator Q a 5 [H, Q a 5] = 0 Q a 5 0 = π a H π a = HQ a 5 0 = Q a 5H 0 = 0 11

12 Phase Diagram: Minimal Version Universality, lattice results T E crossover Plasma 1st order transition ends Hadrons E Nuclear Matter 1 st µ Color Superconductor critical endpoint (E) persists even if m 0 12

13 Transitions without change of symmetry: Liquid-Gas Phase diagram of water Characteristics of a liquid Pair correlation function Good fluid: low viscosity v x liquid gas y F x = ηa v x y 13

14 Transitions without change of symmetry: Gas-Plasma Phase diagram of hydrogen Plasma Effects Debye screening R D V (r) = e r e m Dr m 2 D = 4πe2 n kt Plasma oscillations ω pl = 4πe2 n m 14

15 Fluids: Gases, Liquids, Plasmas,... Hydrodynamics: Long-wavelength, low-frequency dynamics of conserved or spontaneously broken symmetry variables. τ τ micro τ λ 1 Historically: Water (ρ, ɛ, π) 15

16 Example: Simple Fluid Conservation laws: mass, energy, momentum ρ t + (ρ v) = 0 ɛ t + j ɛ = 0 t (ρv i) + x j Π ij = 0 [Euler/Navier-Stokes equation] Constitutive relations: Energy momentum tensor Π ij = P δ ij + ρv i v j + η ( i v j + j v i 23 ) δ ij k v k +... reactive dissipative 16

17 Weakly Coupled Fluids: Kinetics Weakly coupled fluid Collection of Quasi-Particles lmfp lpp and E Γ Introduce distribution function fp(x, t) N = d 3 p (2π) 3 1 2Ep fp Tij = d 3 p (2π) 3 pipj 2Ep fp 17

18 Transport from Kinetics Boltzmann equation f p t + v x f p + F p f p = C[f p ] Collision term C[f p ] = C gain C loss p q p q p q p q p q p q Linearized theory (Chapman-Enskog): f p = f 0 p (1 + χ p /T ) suitable for transport coefficients shear viscosity χ p = g p p x p y x v y 18

19 Effective Theories for Fluids (Here: Weak Coupling QCD) L = q f (id/ m f )q f 1 4 Ga µνg a µν f p t + v x f p = C[f p ] (ω < T ) t (ρv i) + x j Π ij = 0 (ω < g 4 T ) 19

20 And now for something completely different... 20

21 Gauge Theory at Strong Coupling: Holographic Duals The AdS/CFT duality relates large N c (Conformal) gauge theory in 4 dimensions correlation fcts of gauge invariant operators exp dx φ 0 O = string theory on 5 dimensional Anti-de Sitter space S 5 boundary correlation fcts of AdS fields Z string [φ( AdS) = φ 0 ] The correspondence is simplest at strong coupling g 2 N c strongly coupled gauge theory classical string theory 21

22 Holographic Duals at Finite Temperature Thermal (conformal) field theory AdS 5 black hole CFT temperature Hawking temperature of black hole CFT entropy Hawking-Bekenstein entropy area of event horizon s weak coupling strong coupling λ = g 2 N s(λ ) = π2 2 N 2 c T 3 = 3 4 s(λ = 0) Gubser and Klebanov 22

23 Holographic Duals: Transport Properties Thermal (conformal) field theory AdS 5 black hole CFT entropy shear viscosity Strong coupling limit Hawking-Bekenstein entropy area of event horizon Graviton absorption cross section area of event horizon η s η s = 4πk B Son and Starinets PSfrag replacements h 4πk B Strong coupling limit universal? Provides lower bound for all theories? 0 g 2 N c 23

24 Effective Theories (Strong coupling) L = λ(iσ D)λ 1 4 Ga µνg a µν +... S = 1 2κ 2 5 d 5 x gr +... t (ρv i) + x j Π ij = 0 (ω < T ) 24

25 Kinetics vs No-Kinetics Spectral function ρ(ω) = ImG R (ω, 0) associated with T xy 1 ρ xyxy (ω) s 2ω 0.6 1/g 4 (ω/t ) AdS/CFT π(ω/2πt) /s ρ xyxy (ω)/2ω g η/s=1/4π g 4 T g 2 T gt T weak coupling QCD ω ω/2πt strong coupling AdS/CFT transport peak vs no transport peak 25

26 Summary (Theory) Lattice QCD: single chiral and deconfinement crossover transition T c 185 MeV, ɛ cr 1.5 GeV/fm 3 Weakly coupled Quark Gluon Plasma Quark and gluon quasi-particles, γ ω Thermodynamics: Stefan-Boltzmann gas Transport: long equilibration times, η/s 1/α 2 s 1 Strongly coupled plasma No quasi-particles, no kinetics, only hydrodynamics Thermodynamics: Stefan-Boltzmann law Transport: fast equilibration, η/s 1/(4π) < 1 26