Visualization of Topological Structure and Chiral Condensate *

We perform a mutual analysis of the topological and chiral vacuum structure of four-dimensional QCD on the lattice at finite temperature. We demonstrate that at the places where instantons are present, amplified production of quark condensate takes place. It turns out for full QCD that the clusters of nontrivial chiral condensate have a size of about 0.4 fm corresponding to the instanton sizes in the same configurations. It is well known that the zero eigenvalues of the fermionic matrix are related to the global topo-logical charge Q of a gauge field configuration via the Atiyah-Singer index theorem. It is believed that the instantons as carriers of the topological charge might play a crucial role in understanding the confinement mechanism of four-dimensional QCD, if one assumes that they form a so-called in-stanton liquid [1]. Recently, it was demonstrated that monopole currents appear preferably in the regions of non-vanishing topological charge density [2,3]. It has been conjectured that both in-stantons and monopoles are related to chiral symmetry breaking [1,4]. This idea is further supported by the following results of a direct investigation of the local correlations of the quark con-densate and the topological charge density. For the implementation of the topologi-cal charge on a Euclidian lattice we restrict ourselves to the so-called field theo-retic definitions which approximate the topolog-ical charge density in the continuum, q(x) = g 2 32π 2 ǫ µνρσ Tr F µν (x)F ρσ (x). We used the pla-quette and the hypercube prescription. To get rid of quantum fluctuations and renormalization constants , we employed the Cabbibo-Marinari cooling method. Mathematically and numerically the local chiral condensate ¯ ψψ(x) is a diagonal element of the inverse of the fermionic matrix of the QCD action. We compute correlation functions between two observables O 1 (x) and O 2 (y)