Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North...

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The “Big” Picture Thomas Schaefer North Carolina State University 1

Transcript of Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North...

Page 1: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

The “Big” Picture

Thomas Schaefer

North Carolina State University

1

Page 2: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

“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

Page 3: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

What is QCD (Quantum Chromo Dynamics)?

Elementary fields: Quarks Gluons

(qα)af

color a = 1, . . . , 3

spin α = 1, 2

flavor f = u, d, s, c, b, t

Aaµ

color a = 1, . . . , 8

spin ε±µ

Dynamics: Generalized Maxwell (Yang-Mills) + Dirac theory

L = q̄f (iD/ −mf )qf − 1

4Ga

µνGaµν

Gaµν = ∂µA

aν − ∂νA

aµ + gfabcAb

µAcν

iD/ q = γµ(

i∂µ + gAaµt

a)

q

3

Page 4: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

“Seeing” Quarks and GluonsM

ade on 28-Aug-1996 13:39:06 by D

RE

VE

RM

AN

N w

ith DA

LI_D

7.Filenam

e: DC

015768_005906_960828_1338.PS_2J_3J

DALI

Run=9063 Evt=7848 ALEPH Run=15768 Evt=5906

e−

e+

q

q

e−

e+

q

g

q

4

Page 5: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Asymptotic Freedom

Classical field Aclµ . Modification due to quantum fluctuations:

Aµ = Aclµ + δAµ

1

g2F 2

cl →(

1

g2+ c log

(

k2

µ2

))

F 2

cl

Aclµ (k) Acl

ν (k)

(2p + k)µ kνFµν (2p + k)µ

δAµ(p) δAµ δΦ

dielectric ε > 1 paramagnetic µ > 1 dielectric ε > 1

µε = 1 ⇒ ε < 1

β(g) =∂g

∂ log(µ)=

g3

(4π)2

{[1

3− 4

]

Nc +2

3Nf

}

< 0

5

Page 6: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Running Coupling Constant

6

Page 7: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

What is a Phase of QCD? Phases of Gauge Theories

Coulomb Higgs Confinement

� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �

V (r) ∼ −e2

rV (r) ∼ −e

−mr

rV (r) ∼ kr

Standard Model: U(1) × SU(2) × SU(3)

7

Page 8: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

What is a Phase of QCD? Phases of Gauge Theories

Coulomb Higgs Confinement

� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �

V (r) ∼ −e2

rV (r) ∼ −e

−mr

rV (r) ∼ kr

QCD: High T phase High µ phase Low T, µ phase

8

Page 9: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Phases of Matter: Symmetries

phase order broken rigidity Goldstoneparam symmetry phenomenon boson

crystal ρk translations rigid phonon

magnet ~M rotations hysteresis magnon

superfluid 〈Φ〉 particle number supercurrent phonon

supercond. 〈ψψ〉 gauge symmetry supercurrent none (Higgs)

χsb 〈ψ̄ψ〉 chiral symmetry axial current pion

9

Page 10: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Chiral Symmetry

Define left and right handed fields

ψL,R =1

2(1 ± γ5)ψ

L

R

Fermionic lagrangian, M = diag(mu,md,ms)

L = ψ̄L(iD/ )ψL + ψ̄R(iD/ )ψR

+ ψ̄LMψR + ψ̄RMψL

L RL

L R R L

R

M M

M = 0: Chiral symmetry (L,R) ∈ SU(3)L × SU(3)R

ψL → LψL, ψR → RψR

10

Page 11: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Chiral Symmetry Breaking

Chiral symmetry is spontaneously broken

〈ψ̄fLψ

gR + ψ̄f

LψgR〉 ' −(230 MeV)3 δfg

SU(3)L × SU(3)R → SU(3)V (G→ H)

Consequences: dynamical mass generation mQ = 300 MeV À mq

mN = 890 MeV + 45 MeV (QCD, 95%) + (Higgs, 5%)

Goldstone Bosons: Consider broken generator Qa5

[H,Qa5] = 0 Qa

5|0〉 = |πa〉 H|πa〉 = HQa

5|0〉 = Qa

5H|0〉 = 0

11

Page 12: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Phase Diagram: Minimal Version

Plasma

T

µ

Hadrons

Nuclear Matter

Color Superconductor

1 st

E

lattice results

Universality,

1st order transition ends

E

crossover

critical endpoint (E) persists even if m 6= 0

12

Page 13: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Transitions without change of symmetry: Liquid-Gas

Phase diagram of water Characteristics of a liquid

Pair correlation function

2 4 6 8 10 12 14

0.2

0.4

0.6

0.8

1

1.2

1.4

liquid

gas

Good fluid: low viscosity

y

vx

Fx = ηA∂vx∂y

13

Page 14: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Transitions without change of symmetry: Gas-Plasma

Phase diagram of hydrogen Plasma Effects

Debye screening

RD

V (r) = −ere−mDr

m2

D =4πe2n

kTPlasma oscillations

ωpl =4πe2n

m

14

Page 15: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Fluids: Gases, Liquids, Plasmas, . . .

Hydrodynamics: Long-wavelength, low-frequency

dynamics of conserved or spontaneously broken sym-

metry variables.

τ ∼ τmicro τ ∼ λ−1

Historically: Water

(ρ, ε, ~π)

15

Page 16: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Example: Simple Fluid

Conservation laws: mass, energy, momentum

∂ρ

∂t+ ~∇(ρ~v) = 0

∂ε

∂t+ ~∇~ ε = 0

∂t(ρvi) +

∂xj

Πij = 0

[Euler/Navier-Stokes equation]

Constitutive relations: Energy momentum tensor

Πij = Pδij + ρvivj + η

(

∂ivj + ∂jvi −2

3δij∂kvk

)

+ . . .

reactive dissipative

16

Page 17: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Weakly Coupled Fluids: Kinetics

Weakly coupled fluid ≡ Collection of Quasi-Particles� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � �lmfp À lpp and E À Γ

Introduce distribution function fp(x, t)

N =

d3p

(2π)31

2Ep

fp Tij =

d3p

(2π)3pipj

2Ep

fp

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Page 18: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Transport from Kinetics

Boltzmann equation

∂fp

∂t+ ~v · ~∇xfp + ~F · ~∇pfp = C[fp]

Collision term C[fp] = Cgain − Closs

p′

p

q′

q

p′

p

q′

q

p′

p

q′

q

Linearized theory (Chapman-Enskog): fp = f0

p (1 + χp/T )

suitable for transport coefficients

shear viscosity χp = gppxpy∂xvy

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Page 19: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Effective Theories for Fluids (Here: Weak Coupling QCD)

L = q̄f (iD/ −mf )qf − 1

4Ga

µνGaµν

∂fp

∂t+ ~v · ~∇xfp = C[fp] (ω < T )

∂t(ρvi) +

∂xj

Πij = 0 (ω < g4T )

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Page 20: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

And now for something completely different . . .

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Page 21: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Gauge Theory at Strong Coupling: Holographic Duals

The AdS/CFT duality relates

large Nc (Conformal) gauge

theory in 4 dimensions⇔

string theory on 5 dimensional

Anti-de Sitter space ×S5

correlation fcts of gauge

invariant operators⇔ boundary correlation fcts

of AdS fields

〈exp

dx φ0O〉 =

Zstring[φ(∂AdS) = φ0]

The correspondence is simplest at strong coupling g2Nc

strongly coupled gauge theory ⇔ classical string theory

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Page 22: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Holographic Duals at Finite Temperature

Thermal (conformal) field theory ≡ AdS5 black hole

CFT temperature ⇔ Hawking temperature of

black hole

CFT entropy ⇔ Hawking-Bekenstein entropy

∼ area of event horizon

s

λ = g N2

weak coupling

strong coupling

s(λ→ ∞) =π2

2N2

c T3 =

3

4s(λ = 0)

Gubser and Klebanov

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Page 23: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Holographic Duals: Transport Properties

Thermal (conformal) field theory ≡ AdS5 black hole

CFT entropy ⇔ Hawking-Bekenstein entropy

∼ area of event horizon

shear viscosity ⇔ Graviton absorption cross section

∼ area of event horizon

Strong coupling limit

η

s=

~

4πkB

Son and Starinets

PSfrag replacements

0

4πkB

η

s

g2Nc

Strong coupling limit universal? Provides lower bound for all theories?

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Page 24: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Effective Theories (Strong coupling)

L = λ̄(iσ ·D)λ− 1

4Ga

µνGaµν + . . . ⇔ S =

1

2κ2

5

d5x√−gR + . . .

∂t(ρvi) +

∂xj

Πij = 0 (ω < T )

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Page 25: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Kinetics vs No-Kinetics

Spectral function ρ(ω) = ImGR(ω, 0) associated with Txy

ω

1s

ρxyxy(ω)2ω

∼ 1/g4

∼ 1

∼ g2

∼ 1

∼ (ω/T )3

g4T g2T gT T 0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

1/s

ρxyxy

(ω)/

2ωω/2πT

η/s=1/4π

AdS/CFT

π(ω/2πT)3

weak coupling QCD strong coupling AdS/CFT

transport peak vs no transport peak

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Page 26: Big Picture - Department of Physics · 2009. 3. 27. · The \Big" Picture Thomas Schaefer North Carolina State University 1 \Big" Questions What is QCD? What is a Phase of QCD? What

Summary (Theory)

Lattice QCD: single chiral and deconfinement crossover transition

Tc ∼ 185 MeV, εcr ∼ 1.5 GeV/fm3

Weakly coupled Quark Gluon Plasma

Quark and gluon quasi-particles, γ ¿ ω

Thermodynamics: Stefan-Boltzmann gas

Transport: long equilibration times, η/s ' 1/α2

s À 1

Strongly coupled plasma

No quasi-particles, no kinetics, only hydrodynamics

Thermodynamics: Stefan-Boltzmann law

Transport: fast equilibration, η/s ' 1/(4π) < 1

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