スライド 1 - uni-bielefeld.de
Download
Report
Transcript スライド 1 - uni-bielefeld.de
QGP and Confinement
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
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.
Let us think
together !
Data are
preliminary.
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)
Who has seen the Mag. Monopole ?
N
S
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
~3
d F d F
3
~
F F
d
d FF
d
FF~ d
d
FF d
FF T r F F
~
~
FF T r F F
Wilson Loops for a charge
t
-e
+e
R
Surface Operator
Center Projection
Del Debbio, Faber, Giedt, Greensite, Olejnik
Phys.Rev. D58, 1998, 094501
Max T rU ( x)
x,
Max
Tr U
Landau gauge or
Coulomb Gauge
Z ( x) sign TrU ( x) 1 or 1
Gauge Rotation.
Therefore non-local
2
1 Z 2
1 Z 2
Plaquette pierced by a Vortex
If Z Z Z Z 1
1-d
Object
(Charge)
Wilson
Loop
A Vortex pierces
the Plaquette.
2-d Object
(Vortex Line)
Wilson
Loop
Vortex Removing
U ( x) Z ( x) U ( x)
Remember that
By definition, now
Z ( x) sign TrU ( x)
sign TrU ( x) 1 for all links.
All vortices are fading out (by definition).
Surface Operator
d
d FF
d
Operator A
FF~ d
d
FF d
Operator B
Size Dependence of Operator A
<
A
>
L
L
Size Dependence of Operator A
with/without the Vortices
After removing Vortices
L
Fitting
2.000
11.2632 L
2.000
10.3888 L
L
Size Dependence of OperatorB
<
B
>
L
L
Size Dependence of Operator B
with/without the Vortices
<
B
>
L
L
A
L=1
A
R
R
No Vortex
Removal
A
A
With and Without
Vortices
R
R
A
L=1,2,3
A
R
R
B
B
With and Without
Vortices
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
1995
1995
1998
SU(3)
Improved Action
2005
U(1)
Coulomb and
Confinement
Phases
SU(2)
Two Definitions:
F=log U
F=U-1
The first calculation
of eta/s on the lattice,
which is consistento
with KSS bound.
Viscosity by Lattice, 2007
h: shear viscosity
s: Entroypy density
Nakamura and Sakai
c
Fluctuations in MC sweeps
Standard Action
Improved
Action
中川君のデータ２
T / Tc 4
T / Tc 5
One Talk, One Topics !
This is SU(3) resuts !
Sorry ! Let us come back to SU(2) .
T12 (0)T12 (t )
Standard Plaq.
Action
601000Sweeps
3.0 (T / Tc 5.1)
t
163 8
SU (2)
T12 (0)T12 (t )
With Multi-Hit
t
T12 (0)T12 (t )
With Multi-Hit
+ Vortex Removal
t
T12 (0)T12 (t )
Improve Action
(Symanzik)
2.2 (T / Tc 2.5)
163 8
SU (2)
60000100Sweeps
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 !