Study of the structure of the QCD vacuum

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

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

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

Confinement The model (Mandelstam& ‘t Hooft, ’ 75) The dual Meissner effect Analogy of a superconductor Abelian projection (‘t. Hooft, ’ 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, PRD 68(2003)

Confinement Gauge dependence? Landau gauge Local unitary gauge (F 12 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)

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

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

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

Numerical setup preliminary

Numerical results Spectral density 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. . )

Topological charge Numerical results preliminary 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

Spectral density preliminary Numerical results

Spectral density preliminary Numerical results

Spectral density preliminary Numerical results

Spectral density Gap Numerical results preliminary

Spectrum of the eigen value preliminary Numerical results

Spectrum of the eigen value preliminary Numerical results

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

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.