Color confinement mechanism and the type of the QCD vacuum

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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)
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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 effect occurs. (80 tHooft)
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2. Lattice QCD study of abelian projection

• When we perform a partial gauge-fixing called
  Maximally abelian (MA) gauge (87 Kronfeld et
  al.), the tHooft-Mandelstam 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)

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• Dual Meissner effect

Electric field flux tube
Monopole current distribution
Dual Meissner picture is seen very beautifully.
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3. gauge-independent?
Is the dual Meissner effect in the infrared
region gauge-independent?
No?

• 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.

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Existence of the linear potential indicates the
flux-squeezing occurs generally in QCD.
Is it understood as the dual Meissner
effect? What squeezes the electric field?
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4.Study of flux in Landau gauge
(T.Suzuki et al, Phys. Rev. Lett. 94, 132001
(2005))

• 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

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Define abelian field strength
MA
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Non-abelian Wilson loops (a source of a Q-Qbar
pair)
Electric field
Magnetic field
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Results 1
Abelian electric field is squeezed also as in
non-abelian one. Other components are almost
zero. Quark-antiquark are located in z direction.
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Results 2 Electric field is squeezed by abelian
magnetic displacement current

Magnetic solenoidal current
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Solenoidal current observed !!!
Landau gauge perpendicular plane
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Landau gauge
Landau gauge MA gauge
MA Gauge
(Bali (98))
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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 confinement mechanism.
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5. Type of the QCD vacuum in MA(Kanazawa
M.Chernodub, M.Polikarpov, V.Zakharov)
The penetration length ( inverse of the dual
photon mass) is fixed from the electric field
flux.
RDistnce between Q and Qbar
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How to determine the coherence length (inverse of
the dual Higgs mass)
Study monopole around QCD string in dual
Ginzburg-Landau theory (Suzuki 1988)
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Behaviors of classical solutions
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place the static quarks at the (spatial)
infinities of the z axis in London limit
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Real world
dominant
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Expected behavior of monopole density around QCD
string
The coherence length can be derived from this
behavior !!
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Numerical data of the coherence length
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Correlation of monopole density and D2 gluon
operator
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Is minimized in MA
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Various D2 gluon operators in MAU(1) LA
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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)
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6. The type of the QCD vacuum in Landau gauge
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Border between type 1 and 2 ? Landau gauge
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7. Study of gauge dependence
Penetration length Coherence
length
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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.

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• Existence of the dual Meissner effect suggests
  that something magnetic condenses in the vacuum.
  Gauge-invariant monopoles are working? Extraction
  of monopole need not always abelian projection.
  Or essentially non-static?
• 1. Gubarevs monopoles may be important and
  should be studied extensively.(Gubarev,
  hep-lat/0204018, Gubarev-Zakharov
  hep-lat/0204017)
• 2. Violation of non-abelian Bianchi identity may
  be important?(Gubarev Morozov, hep-lat/0503023)

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• D2 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