QGP and Confinement

XQCD 2010Wilhelm and Else Heraeus Seminar

Bad Honnef, June 21-23

X-QCD Japan (S.Motoki, K.Nagata, Y.Nakagawa,

A. Nakamura and T.Saito)and

V.I.Zakharov

Poster

Next Talk

I am very proud that

Most of the Results here are New!

I regret that

?I do not know the Meaning of the most data.

Data are preliminary.

Let us think together !

Most data are Quench and color SU(2)

Magnetic Degrees of Freedom and the Confinement

• G.t’Hooft, Nucl.Phys. B190 (1981) 455• H Shiba and T Suzuki. Phys. Lett. B (1994) 461• A. Di Giacomo and G. Paffuti, Phys.Rev.D56,6816 (1997)• Kei-ichi Kondo, Phys.Rev.D58,105019 (1998)• …..• J. Liao and E. Shuryak, Phys.Rev.Lett.,101, 162302 (2008)• M.N. Chernodub and V.I. Zakharov, Phys. Rev. Lett.98,

082002 (2007)• M.N. Chernodub, A. Nakamura and V.I. Zakharov

Phys.Rev.D78:074021,2008• M.N. Chernodub and V.I. Zakharov,

Phys.Atom.Nucl.72:2136-2145,2009 (arXiv:0806.2874)

NS

Who has seen the Mag. Monopole ?

Neither I nor you

Spin System

Singular Configuration, or Vortex

No Monopole !But it looks like ,,,

Vortices related to the Confinemen are a 2-d Object and we need

Surface Operator

• S.Gukov and E.Witten, hep-th/0612073.E.Wittten, Fortsch. Phys. 55 (2007) 545.

• A.DiGiacomo and V.I.Zakharov, hep-th/0806.29382

33 ~ FdFd

d

d

FF

FFd

d

dFFd

~

FF ~

FFFF Tr

FFFF~

Tr ~

Wilson Loops for a charge

+e -e

R

t

Surface Operator

Center Projection

)(Tr Max,

xUx

2Tr Max U

Landau gauge or Coulomb Gauge

21 Z

21 ZGauge Rotation. Therefore non-local

Del Debbio, Faber, Giedt, Greensite, OlejnikPhys.Rev. D58, 1998, 094501

1or 1)(Tr sign )( xUxZ

Plaquette pierced by a Vortex

1 If ZZZZ

A Vortex pierces the Plaquette.

1-d Object(Charge)

Wilson Loop

2-d Object (Vortex Line)

Wilson Loop

Vortex Removing

)()()( xUxZxU

)(Tr sign )( xUxZ Remember that

By definition, now links. allfor 1)(Tr sign xU

All vortices are fading out (by definition).

Surface Operator

d

d

FF

FFd

d

dFFd

~

Operator A Operator B

Size Dependence of Operator A

LA< >

L

Size Dependence of Operator Awith/without the Vortices

After removing Vortices

L

Fitting

000.23888.10 L

000.22632.11 L

L

Size Dependence of OperatorB

LB< >

L

Size Dependence of Operator Bwith/without the Vortices

LB< >

L

A A

R

R

L=1No Vortex Removal

A A With and WithoutVortices

R

R

A A L=1,2,3

R

R

B B With and WithoutVortices

R

Another Possibility (in Future)

Transport Coefficients

One of X-QCD Japan projects is to calculate Transport Coefficients at RHIC and LHC temperature regions and to see if they are different. What does “Perfect Fluid” mean ?

History

U(1)Coulomb and Confinement Phases

SU(2)

Two Definitions:

F=log U

F=U-1

SU(3)

Improved Action

1995 1995 1998

2005

The first calculation of eta/s on the lattice, which is consistento with KSS bound.

c

Viscosity by Lattice, 2007

Nakamura and Sakai

h: shear viscosity

s: Entroypy density

Fluctuations in MC sweeps

Standard Action

Improved Action

中川君のデータ２

4/ cTT

5/ cTT

One Talk, One Topics !This is SU(3) resuts !

Sorry ! Let us come back to SU(2) .

)2(

816

)1.5/( 0.33

SU

TT c

)()0( 1212 tTT

t

Sweeps 100060

Standard Plaq. Action

With Multi-Hit

)()0( 1212 tTT

t

With Multi-Hit+ Vortex Removal

)()0( 1212 tTT

t

Improve Action (Symanzik)

)2(

816

)5.2/( 2.23

SU

TT c

Sweeps 10060000

)()0( 1212 tTT

Conclusion

• QCD is a Quantum Field Theory.• QCD has a very special feature,

the Confinement.• If a singular structure of the quantum field (gluon

field) explains the confinement, it is very interesting (at least to me).

• The surface operators feel Vortex.• Transport Coefficients change if we remove the

Vortex.• We want to understand QGP natures in terms of

the Surface operators in future.

In other words,

QCD/QGP physics provides an opportunity to see a new quantum field mechanism, the singularities on surfaces.

Many Thanks Frithjof, Krzysztof and Christian

for this nice seminar !