Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Status of Strong Coupling Lattice QCD in Exploring QCD Phase
Diagram
KOHTARHO. MIURA
YITP

12/26(Fri), 2008, Talk in Kyusyu Univ.

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

QCD Phase Diagram

T

Early
Universe

RHIC
LHC

QGP

∼ 190
MeV

LQCDMCAGS

HadronCSC ?
Quarkyonic?

Our
World

Nucleus

NeutronStar

KOHTARHO. MIURA

ρStatus of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice MC.

ModelsSC-LQCD

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Table of Contents
1

Introduction (5 min.)2

Confinement and Deconfinement (10 min.)Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop3

Chiral Phase Transition (10 min.)1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

4

Recent Developments (20 min)Phase Diagram
Viscosity

5

Summary and Future Developments

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Table of Contents
1

Introduction (5 min.)2

Confinement and Deconfinement (10 min.)Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop3

Chiral Phase Transition (10 min.)1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

4

Recent Developments (20 min)Phase Diagram
Viscosity

5

Summary and Future Developments

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Lattice QCD Action (Pure Glue)

Plaquette2Uνρ,x ∼ eia g Gνρ,xAction for Pure GlueZ
X 2Nc h
˜i
1
trc ˆ
†
SG =
→
1
−
U
+
U
d 4 x Gνρ,x Gxνρ
νρ,x
νρ,x
2
g
2N
4
c
νρ,x

KOHTARHO. MIURA(1)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Lattice QCD Action (Pure Glue)

Plaquette2Uνρ,x ∼ eia g Gνρ,xAction for Pure GlueZ
X 2Nc h
˜i
1
trc ˆ
†
SG =
→
d 4 x Gνρ,x Gxνρ
1
−
U
+
U
νρ,x
νρ,x
2
4
g
2N
c
νρ,x

KOHTARHO. MIURA(1)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Lattice QCD Action (Pure Glue)

Plaquette2Uνρ,x ∼ eia g Gνρ,xAction for Pure GlueZ
X 2Nc h
˜i
1
trc ˆ
†
SG =
→
d 4 x Gνρ,x Gxνρ
1
−
U
+
U
νρ,x
νρ,x
2
4
g
2N
c
νρ,x

KOHTARHO. MIURA(1)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Wilson Loop (Wilson (1974))

···

...
Nτ

W

...

...

( Nc1g2 )Nτ L

···
1/g 2
expansion

···
···

R

DU da

b
c

= (1/Nc )δab δcd

LZ
hW [U]i∝˜ˆ
DU W [U] exp −SG [U ] ' exp[−Nτ V]

V = L log[Nc g 2 ]KOHTARHO. MIURA(2)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Wilson Loop (Wilson (1974))

···

...
Nτ

W

...

...

( Nc1g2 )Nτ L

···
1/g 2
expansion

···
···

R

DU da

b
c

= (1/Nc )δab δcd

LZ
hW [U]i∝˜ˆ
DU W [U] exp −SG [U ] ' exp[−Nτ V]

V = L log[Nc g 2 ]KOHTARHO. MIURA(2)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Wilson Loop (Wilson (1974))

···

...
Nτ

W

...

...

( Nc1g2 )Nτ L

···
1/g 2
expansion

···
···

R

DU da

b
c

= (1/Nc )δab δcd

LZ
hW [U]i∝˜ˆ
DU W [U] exp −SG [U ] ' exp[−Nτ V]

V = L log[Nc g 2 ]KOHTARHO. MIURA(2)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Wilson Loop (Wilson (1974))

···

...
Nτ

W

...

...

( Nc1g2 )Nτ L

···
1/g 2
expansion

···
···

R

DU da

b
c

= (1/Nc )δab δcd

LZ
hW [U]i∝˜ˆ
DU W [U] exp −SG [U ] ' exp[−Nτ V]

V = L log[Nc g 2 ]KOHTARHO. MIURA(2)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

String tension
SU(2) String Tension(Munster (1981))
Weak coupling
leading
Strong coupling
leadinga2σ

Dots=Lattice MC.
Creutz (1979)

S trong coupling regime

would be smoothly connectedwith the perturbative regime.

12-th order ofStrong coupling exp.
Munster (1981)

S trong coupling expansion
was complimentary to
the lattice MC, and vice versa.

β = 2Nc/g 2
KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Polyakov Loop

L̄P
W

LP
τ
R3

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop

Potential of Polyakov Loop (SU(Nc = 3))
SU(2): Polonyi,Szlachanyi(1982) , SU(3): Gross, J. Bartholomew, and D. Hochberg(1983)
c.f. PNJL (Fukushima (2003))

ˆ˜
VP /T = −2d e −aσ/T Nc2 l̄P lP − log 1 − 6l̄P lP − 3(l̄P lP )2 + 4(lP3 + l̄P3 )

0.3

(3)

C2=4.2C2=4.7C2=5.2

0.2

Vp

0.1
0
-0.1
-0.2
0

0.1

0.2

KOHTARHO. MIURA

0.3 0.4
|lp|

0.5

0.6

0.7

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

Table of Contents
1

Introduction (5 min.)2

Confinement and Deconfinement (10 min.)Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop3

Chiral Phase Transition (10 min.)1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

4

Recent Developments (20 min)Phase Diagram
Viscosity

5

Summary and Future Developments

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

1/g 2 & 1/d expansion
Pioneering Works: Kawamoto,Smit (’81), Kluberg-Stern,Moreo,Napoly,Peterson(’81)
1/d expansion: Kluberg-Stern,Moreo,Peterson(’83)

ZLQCD = χ,χ̄,U exp[−SF − SG ]
R

χ̄

R

Uν

χ

1/g 2

DUν with 1/g 2 expansion
M

M B̄

B

M

M

M

M

P
P
P
ν<ρ MMMM,
ν Mx Mx+ν̂ ,ν B̄x Bx+ν̂ ,exp[−Seff [

0

0

0

−1/2

O(g , d ) O(g , d

KOHTARHO. MIURA

etc]) O(g −2, d0)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

Hadron Mass Spectrum
Staggered Hadrons: Kluberg-Stern,Moreo,Peterson(’83), Golterman,Smit(’85)

Kluberg-Stern-Morel-Petersson(1983)

Strong Coupling Expansion is consistent with the lattice MC and experiments !!

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

T and µPolyakov Gauge

τ
1

2

3

U0,x = diag{eiθx T , eiθx T , eiθx T }R3

Lattice Chemical Potential Karsch,Hasenfratz (’83)
U0 → e µ U0 ,KOHTARHO. MIURA(c.f . iA0 → iA0 + µ)

(4)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

T and µPolyakov Gauge

τ
1

2

3

U0,x = diag{eiθx T , eiθx T , eiθx T }R3

Lattice Chemical Potential Karsch,Hasenfratz (’83)
U0 → e µ U0 ,KOHTARHO. MIURA(c.f . iA0 → iA0 + µ)

(4)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

Phase Diagram

Damgaard-Kawamoto-Shigemoto (1986)

Damgaard-Hochberg-Kawamoto (1985)

1100 (MeV)
2nd order

290 (MeV)
1st order

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

Some Comments

Effective Potential
Damgaard,Kawamoto,Shigemoto(’86), Faldt,Petersson (’86)
Veff =

h sinh[(N + 1)E /T ]id 2c
σ − T log
+ 2 cosh[Nc µ/T ]4Ncsinh[E /T ](5)

Phase Diagrams
Bilic,Karsch,Redlich (1992)
Bilic,Demeterfi,Peterson (1992)
Bilic,Cleymens (1995)

Related Models
Ilgenfritz,Kripfganz(1985)
Gocsh,Ogilve (1986)

Monomer-Dimer-Polymer
Dagotto,Moreo,Wolf (1986,87)
Karsch,Mutter (1990)

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Table of Contents
1

Introduction (5 min.)2

Confinement and Deconfinement (10 min.)Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop3

Chiral Phase Transition (10 min.)1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

4

Recent Developments (20 min)Phase Diagram
Viscosity

5

Summary and Future Developments

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Strong Coupling Limit SU(2)µµNishida-Fukushima-Hatsuda (2003) SU(Nc = 2), Strong coupling limit

Pauli-Gursey (σ ↔ ∆) symmetry at (m0 , µ) = (0, 0). m0 favors σ, µfavors ∆. Saturation effect.
Similar phase diagram is obtained in SU(Nc = 3) with isospin chemical
pot. (σ ↔ π) (Nishida ’04).
The diquark has not been realized in SU(Nc = 3). (c.f. Diquarks in SU(3):Azcoiti et al. (2003))

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Strong Coupling Limit SU(2)µµNishida-Fukushima-Hatsuda (2003) SU(Nc = 2), Strong coupling limit

Pauli-Gursey (σ ↔ ∆) symmetry at (m0 , µ) = (0, 0). m0 favors σ, µfavors ∆. Saturation effect.
Similar phase diagram is obtained in SU(Nc = 3) with isospin chemical
pot. (σ ↔ π) (Nishida ’04).
The diquark has not been realized in SU(Nc = 3). (c.f. Diquarks in SU(3):Azcoiti et al. (2003))

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Strong Coupling Limit SU(2)µµNishida-Fukushima-Hatsuda (2003) SU(Nc = 2), Strong coupling limit

Pauli-Gursey (σ ↔ ∆) symmetry at (m0 , µ) = (0, 0). m0 favors σ, µfavors ∆. Saturation effect.
Similar phase diagram is obtained in SU(Nc = 3) with isospin chemical
pot. (σ ↔ π) (Nishida ’04).
The diquark has not been realized in SU(Nc = 3). (c.f. Diquarks in SU(3):Azcoiti et al. (2003))

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Strong Coupling Limit SU(2)µµNishida-Fukushima-Hatsuda (2003) SU(Nc = 2), Strong coupling limit

Pauli-Gursey (σ ↔ ∆) symmetry at (m0 , µ) = (0, 0). m0 favors σ, µfavors ∆. Saturation effect.
Similar phase diagram is obtained in SU(Nc = 3) with isospin chemical
pot. (σ ↔ π) (Nishida ’04).
The diquark has not been realized in SU(Nc = 3). (c.f. Diquarks in SU(3):Azcoiti et al. (2003))

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Strong Coupling Limit SU(2)µµNishida-Fukushima-Hatsuda (2003) SU(Nc = 2), Strong coupling limit

Pauli-Gursey (σ ↔ ∆) symmetry at (m0 , µ) = (0, 0). m0 favors σ, µfavors ∆. Saturation effect.
Similar phase diagram is obtained in SU(Nc = 3) with isospin chemical
pot. (σ ↔ π) (Nishida ’04).
The diquark has not been realized in SU(Nc = 3). (c.f. Diquarks in SU(3):Azcoiti et al. (2003))

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Strong Coupling Limit SU(2)µµNishida-Fukushima-Hatsuda (2003) SU(Nc = 2), Strong coupling limit

Pauli-Gursey (σ ↔ ∆) symmetry at (m0 , µ) = (0, 0). m0 favors σ, µfavors ∆. Saturation effect.
Similar phase diagram is obtained in SU(Nc = 3) with isospin chemical
pot. (σ ↔ π) (Nishida ’04).
The diquark has not been realized in SU(Nc = 3). (c.f. Diquarks in SU(3):Azcoiti et al. (2003))

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Strong Coupling Limit SU(2)µµNishida-Fukushima-Hatsuda (2003) SU(Nc = 2), Strong coupling limit

Pauli-Gursey (σ ↔ ∆) symmetry at (m0 , µ) = (0, 0). m0 favors σ, µfavors ∆. Saturation effect.
Similar phase diagram is obtained in SU(Nc = 3) with isospin chemical
pot. (σ ↔ π) (Nishida ’04).
The diquark has not been realized in SU(Nc = 3). (c.f. Diquarks in SU(3):Azcoiti et al. (2003))

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Strong Coupling Limit SU(3)Fukushima(’04), Nishida(’04), Kawamoto-Miura-Ohnishi-Ohnuma(’05)
Fukushima (2004)
SU(Nc = 3), Strong coupling limit
Kawamoto-Miura-Ohnishi-Ohnuma (’07)
SU(Nc = 3), Strong coupling limit

1st and 2nd transitions with tri-critical point appear!!

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Strong Coupling Limit SU(3)Fukushima(’04), Nishida(’04), Kawamoto-Miura-Ohnishi-Ohnuma(’05)
Fukushima (2004)
SU(Nc = 3), Strong coupling limit
Kawamoto-Miura-Ohnishi-Ohnuma (’07)
SU(Nc = 3), Strong coupling limit

1st and 2nd transitions with tri-critical point appear!!

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Energy scale modifications due to 1/g 2

A Plaquette Effect and MFA
A Diagram with 1/g 2
χ

e

U0†

χ̄

χ̄

eµ U0

χ

−µ

Mean Fields

Physical Meaningϕτ ∼ heµ χ̄U0 χ − e−µ (h.c.)i Quark mass (mq ) suppressionφτ ∼ heµ χ̄U0 χ + e−µ (h.c.)i Quark density (µ suppression)

Energy scale

Tµ mq

KOHTARHO. MIURA

T
1/g 2
effects !!

µmq

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Phase Diagram Evolution with β = 2Nc /g 2
Miura-Kawamoto-Ohnishi, Preliminary

T
µ

mq
Large
Suppression

cri
µcri
T 0 /Tµ=0> 2.0 (real world)

Small
Correction

0.33 Fukushima (’04)
Nishida (’04)∼ 1.0 Present (β ∼ 3.2)
≥ 1.0 MC (Forcrand-Philipsen,
Fodor-Katz, ...)KOHTARHO. MIURA

New Structure !!

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Consistency check(83 × 2)
Forcrand (private comm.)
Kennedy et.al (’85)

0.025

0.05

∞

1.40

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Phase Diagram Evolution with β = 2Nc /g 2

Fukushima (’04)
Nishida (’04)

Miura Ohnishi (Present)

2.0

2nd

Chiral Restored(σ = 0, ρ > 0)

1.0 C < 02

Chiral Broken(σ = σ0 , ρ = 0)

Partially
Chiral Restored(σ  σ0 , ρ > 0)

1st
C2 > 00.0
0.55

β ≥ βc =KOHTARHO. MIURA

2Nc2 (1st)
µc
d

(6)

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Phase Diagram
Viscosity

Shear Viscosity based on SCExp. in Pure Glue

Jakovac Nogradi, arXiv:0810.4181 [hep-th].

w∝T

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Table of Contents
1

Introduction (5 min.)2

Confinement and Deconfinement (10 min.)Lattice QCD Action (Pure Glue)
Wilson Loop
Polyakov Loop3

Chiral Phase Transition (10 min.)1/g 2 & 1/d expansion
Hadron Mass Spectrum
Chiral Phase Transition

4

Recent Developments (20 min)Phase Diagram
Viscosity

5

Summary and Future Developments

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Summary

StatusAn instructive guide for the lattice MC. In particular, “Beyond Sign
Problem” may be urgently required.
Idea source for the model buildings.
Recent developments
Precise structure of the phase diagram at the strong coupling limit (SU(2)and SU(3)).
The phase diagram evolution with the finite coupling.
Shear viscosity in pure glue η/s ∼ 0.25.
Meson mass scalings due to T and µ effects (Miura,Kawamoto Ohnishi(’08)), Banks-Casher relations in SU(2) SC-LQCD at g → ∞ (Fukushima(’08)),Diquark (Azcoiti et al. (’03))etc.

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Summary

StatusAn instructive guide for the lattice MC. In particular, “Beyond Sign
Problem” may be urgently required.
Idea source for the model buildings.
Recent developments
Precise structure of the phase diagram at the strong coupling limit (SU(2)and SU(3)).
The phase diagram evolution with the finite coupling.
Shear viscosity in pure glue η/s ∼ 0.25.
Meson mass scalings due to T and µ effects (Miura,Kawamoto Ohnishi(’08)), Banks-Casher relations in SU(2) SC-LQCD at g → ∞ (Fukushima(’08)),Diquark (Azcoiti et al. (’03))etc.

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram

Introduction (5 min.)Confinement and Deconfinement (10 min.)Chiral Phase Transition (10 min.)Recent Developments (20 min)
Summary and Future Developments

Future Developments

Key Words
Imaginary chemical potential.
Comparison with the lattice MC in the scaling region at µ = 0.
Introducing the SC-LQCD inspired interactions to models.
More sophisticated formulations for diquarks and Viscosity.
Finite T glueball.
Phase diagram for the deconfinement transition.
The density creation in the chiral broken phase.

KOHTARHO. MIURA

Status of Strong Coupling Lattice QCD in Exploring QCD Phase Diagram