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Color confinement mechanism
and
the type of the QCD vacuum
Tsuneo Suzuki (Kanazawa Univ.)
Collaborators:
K.Ishiguro, Y.Mori, Y.Nakamura, T.Sekido
（M.Polikarpov, M.Chernodub, V.Zakharov)
１．Color confinement mechanism
Color confinement could be understood
as the dual Meissner effect. (’75 ‘tHooft &
Mandelstam)
How to find a magnetically charged particle from
QCD?
Perform a partial gauge-fixing called abelian
projection.
QCD is reduced to U(1)2 theory with magnetic
monopoles.
If the monopoles condense, the dual Meissner
2. Lattice QCD study of abelian
projection
When we perform a partial gauge-fixing called Maximally
abelian (MA) gauge (’87 Kronfeld et al.), the ‘tHooftMandelstam conjecture seems to be correct.
1.Abelian dominance, monopole dominance
2. Monopole condensation occurs. Entropy dominates
over energy.
3.The dual Meissner effect is observed clearly.
(M.Chernodub and M.Polikarpov, hep-th/9710205;
T.Suzuki,P.T.P.Suppl.131(‘98)633;
R.W. Haymaker, P.R.315, 153 (‘99),
H.Shiba and T.Suzuki, P.L. B 351, 519 (‘95),
Y.Koma et al, KI & PRD68 (2003) 114504 and references therein)
Dual Meissner effect:
Electric field flux
tube
Monopole current
distribution
Dual Meissner picture is seen very
beautifully.
3. gauge-independent?
Ｉｓ the dual Meissner effect in the
infrared region gaugeindependent?
No?
(1)Polyakov gauge where Polyakov loops are
diagonalized. Monopoles are always static.
Do not contribute to the usual abelian
Wilson loop. Monopole dominance is
broken.(M.Chernodub ’00)
(2)Landau gauge: Configurations are so
smooth. No DeGrand-Toussaint monopoles.
Existence of the linear
potential indicates the fluxsqueezing occurs generally
in QCD.
Is it understood as the dual
Meissner effect?
What squeezes the electric
field?
４．Study
of flux in Landau
gauge
(T.Suzuki et al, Phys. Rev. Lett. 94, 132001 (2005))
1)Imroved Iwasaki gauge action:
Nearer to the continuum limit
2) (Landau) Gauge fixing: study of
electric and magnetic field flux
directly
3) Comparison with MA gauge +
U1 Landau
Define abelian field strength
MA
Non-abelian Wilson loops (a source of a Q-Qbar p
Electric
field
Magnetic
field
Results
1
R
r
Abelian electric field is squeezed also as in nonabelian one. Other components are almost zero.
Quark-antiquark are located in z direction.
Results 2: Electric field is squeezed
by abelian magnetic displacement
current
Magnetic solenoidal
Solenoidal current
observed !!!
Landau gauge perpendicular
plane
Landau gauge
Landau
gauge
MA gauge
MA Gauge
（Bali (’98))
Comments
1.The positions of the peak of the
solenoidal current distribution in Landau
and in MA are almost the same.
2. The dual Meissner effect is observed
also in Landau gauge, where naive DT
lattice
monopoles do not exist. New monopole
or essentially non-static?
The dual Meissner effect must be a
universal
5. Type of the QCD vacuum in
MA
(Kanazawa + M.Chernodub, M.Polikarpov,
The penetration length
( inverse of the dual
V.Zakharov)
photon mass)
is fixed from the electric field flux.
R=Distnce between Q and Qbar
How to determine the coherence
length
(inverse of the dual Higgs mass)
Study monopole around QCD
string in dual Ginzburg-Landau
theory: (Suzuki 1988)
Behaviors of classical solutions
place the static quarks at the
(spatial) infinities of the z axis
London limit
in
Real
world:
dominant
Expected behavior of monopole
density around QCD string
The coherence
length can be
derived from
this behavior !!
Numerical data of the coherence length
Correlation of monopole density and
D=2 gluon operator
Is minimized in MA
Various D=2 gluon operators in MA+U(1)
LA
Border between the type 1 and the type 2
(Cea et al,1995, Singh et al.1993, Matsubara et al.,1994, kato et al.,1998,
Bali 1998, Koma 2003)
6. The type of the QCD vacuum in
Landau gauge
Border between type 1 and 2 ?
Ｌａｎｄａｕ ｇａｕｇｅ
7. Study of gauge dependence
Penetration length
Coherence length
8. Summary and outlook
• The dual Meissner effect works good
also in Landau gauge. How about in
other general gauges? Expectation: It
must work in general.
• Magnetic displacement current plays a
role of monopole currents if we see
naive abelian components.
• The vacuum is near the border of the
type 1 and the type 2.
• Existence of the dual Meissner effect
suggests that something magnetic
condenses in the vacuum. Gaugeinvariant monopoles are working?
Extraction of monopole need not
always abelian projection. Or
essentially non-static?
1. Gubarev’s monopoles may be
important and should be studied
extensively.(Gubarev, hep-lat/0204018, GubarevZakharov hep-lat/0204017)
2. Violation of non-abelian Bianchi
identity may be important?(Gubarev &
Morozov, hep-lat/0503023)
• D=2 gluon condensate operator important?
（１）Consider A+ A in MA gauge:
The effect of the off-diagonal gluons appears
only in the screening of adjoint charged particles.
Fundamental quark confinement is not affected.
(T.Suzuki and M.Chernodub, P.L. B563 (2003) 183)
（２）Ａ３Ａ３： non-perturbative part is given by
monopoles
(3) In LA gauge, both effects are included
in