Instantons and Monopoles in the Nonperturbative QCD

Abstract

We study the confinement physics in QCD in the maximally abelian (MA) gauge using the SU(2) lattice QCD. To clarify the origin of abelian dominance for the long-range physics, we study the charged-gluon propagator in the lattice QCD, and find that the effective mass $m_{ch} \simeq 0.9 {\rm GeV}$ of the charged gluon is induced by the MA gauge fixing. In the MA gauge, there appears the global network of the monopole world-line covering the whole system, which would be identified as monopole condensation at a large scale. To prove monopole condensation, we apply the dual gauge formalism to the monopole part, and derive the inter-monopole potential from the dual Wilson loop in the MA gauge. In the monopole part, which carries the nonperturbative aspects of QCD, the dual gluon mass is evaluated as $m_B \simeq $0.5GeV, which is the evidence of the dual Higgs mechanism by monopole condensation. As for the monopole structure, the large fluctuation of off-diagonal gluons remains around the monopole in the MA gauge, and large cancellation occurs between the diagonal and off-diagonal action densities to keep the total QCD action finite. The charged-gluon rich region around the QCD-monopole would provide the effective monopole size as the critical scale of the abelian projected QCD. Instantons are expected to appear in the charged-gluon rich region around the monopole world-line in the MA gauge, which leads to the local correlation between monopoles and instantons.Comment: Invited Lecture presented by H. Suganuma at 1997 Yukawa International Seminar (YKIS'97) on `` Non-Perturbative QCD -Structure of the QCD Vacuum-'', 2-12 December 1997, in Kyoto, Japan, 12 pages, Plain Late

Infrared abelian dominance and dual Higgs mechanisms in MA gauge

“…From the slope of the logarithmic plot of r 3/2 G off µµ (r) in Fig.1(a), we get the off-diagonal gluon mass as M off ≃ 1.2 GeV in the MA gauge [2,3] as shown in Fig.1(b). Thus, in the MA gauge, the off-diagonal gluon cannot carry the long-range interaction such as the con- * e-mail: suganuma@rcnp.osaka-u.ac.jp finement force.…”

“…As the evidence of the dual Higgs mechanism by color-magnetic monopole condensation, the dual gluon mass is estimated as m B ≃ 0.5 GeV from the lattice data in 0.4 fm < r < 1.5 fm [2]. Here, the dual gluon mass m B ≃ 0.5 GeV provides the key parameter of the DGL theory.…”

“…This is the essence of infrared abelian dominance. In fact, QCD in the MA gauge behaves as a strong-coupling compact QED at the larger scale than M −1 off ≃ 0.2 fm [2,3]. …”

“…Using the SU(2) lattice QCD with 12 3 ×24, 16 4 and 20 4 , we study the off-diagonal gluon propagator G off µµ (r) ≡ A + µ (x)A − µ (y) as the function of r ≡ (x − y) 2 in the MA gauge with U(1) 3 Landau gauge fixing [2,3]. From the slope of the logarithmic plot of r 3/2 G off µµ (r) in Fig.1(a), we get the off-diagonal gluon mass as M off ≃ 1.2 GeV in the MA gauge [2,3] as shown in Fig.1(b).…”

“…(1) Around the QCD-monopole, both the abelian action density S Abel and the off-diagonal gluon contribution S off ≡ S QCD − S Abel are largely fluctuated, and their cancellation keeps the total QCD action density S QCD small [2]. (2) The QCD-monopole has an intrinsic structure relating to a large amount of off-diagonal gluons around its center, similar to the 't Hooft-Polyakov monopole [2].…”