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QGP and Confinement . Poster. X-QCD Japan ( S.Motoki , K.Nagata , Y.Nakagawa , A. Nakamura and T.Saito ) and V.I.Zakharov. XQCD 2010 Wilhelm and Else Heraeus Seminar Bad Honnef , June 21-23. Next Talk. I am ver y proud that. Most of the Results here are New!. I regret that. - PowerPoint PPT Presentation
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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
dd
FFFFd
dd
FFd~
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
dd
FFFFd
dd
FFd~
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24/ 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 !