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

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

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

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)

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)

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

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..)

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

Numerical results Spectral density preliminary

Numerical results Spectral density preliminary

Numerical results Spectral density preliminary

Numerical results Spectral density preliminary Gap

Numerical results Spectrum of the eigen value preliminary

Numerical results Spectrum of the eigen value preliminary

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.

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.