1. Study of the structure of the QCD vacuum
with valence overlap fermions and monopoles.
Toru Sekido
Kanazawa Univ. & RIKEN
( DESY-Kanazawa collaboration )
2007/07/31

2. QCD vacuum Motivation Quark confinement
The quarks cannot be isolated.
Spontaneous Chiral symmetry breaking
Nambu-Goldstone boson

3. QCD vacuum Motivation Finite temperature Quark confinement
order parameter
Polyakov loop
Spontaneous Chiral symmetry breaking
order parameter
Quark condensate

4. The dual Meissner effect
Confinement
(Mandelstam& ‘t Hooft, ’75)
The model
The dual Meissner effect
Analogy of a superconductor
Abelian projection
(‘tHooft,’80)
This seems to be correct
　　　　　　　　　when we perform
Maximally Abelian (MA) gauge.
(Ezawa & Iwasaki,’82 . Kronfeld et al ‘87 . Suzuki,’88 . Suzuki & Maedan,’89 .
Suzuki & Yotsuyanagi,’90 . Hioki et al,’91 . G.Bali, ’98 . etc…)
Y.Koma et al, PRD68(2003)

5. Gauge dependence? Confinement Landau gauge
Local unitary gauge (F12 gauge , Polyakov gauge)
(Suzuki et al,’03 . Sekido et al,’07)
Numerically the feature of the dual Meissner effect was shown
as gauge independent.
(Suzuki et al,’07 and Suzuki’s talk)

6. Abelian and monopoles Abelian projection
Monopoles are responsible for confinement.
Simulation
Gauge fixing condition.
MA gauge fixing for noise reduction.

7. Previous study Chiral property on the Abelian and monopole background.
Fermion condensate in MA gauge
(Miyamura,95)
Quenched SU(2) , finite temperature , valence Staggered fermion
Topological charge in MA gauge
(Sasaki and Miyamura,98)
Quenched SU(2) , valence Wilson fermion
Quenched SU(3) , finite temperature , valence overlap fermion

8. Valence overlap fermion
G-W relation
Overlap Dirac operator
Simulation
Chebyshev polynomial
(50 lowest eigenvalues)

9. Numerical setup
preliminary

10. Spectral density Numerical results Low-lying mode analysis
Topological charge
spectral density
Other works about Low-lying mode and topological defects
(Polikarpov et al ,05 , Kovalenko et al ,05 , Gubarev et al ,05 , etc..)

11. preliminary Topological charge Numerical results
Topological susceptibility.
In Abelian , monopole and photon background,
The number of the zero mode is not always equal to
the absolute value of the topological charge.
non-Abelian case
Abelian (monopole , photon) case
sometime

12. Numerical results
Spectral density
preliminary

13. Numerical results
Spectral density
preliminary

14. Numerical results
Spectral density
preliminary

15. Numerical results
Spectral density
preliminary
Gap

16. Numerical results
Spectrum of the eigen value
preliminary

17. Numerical results
Spectrum of the eigen value
preliminary

18. Summery and future works
The chiral condensate
on non-Abelian ,Abelian ,monopole and photon background.
Non-Abelian
Abelian
monopole
T < Tc : finite chiral condensate
T > Tc : zero chiral condensate
photon
T : zero chiral condensate
It is interesting to investigate the role of the monopole
for chiral symmetry breaking.

19. Summery and future works( )
Increase statistic , several beta points
Full QCD
No gauge fixing
For relation between confinement and chiral symmetry.
Effective action of chiral dynamics and monopole effective action.