Instanton and QCD-monopole Trajectory in the Abelian Dominating System

Correlation between instantons and QCD-monopoles is studied in the abelian-gauge-fixed QCD. From a simple topological consideration, instantons are expected to appear only around the QCD-monopole trajectory in the abelian-dominating system. The QCD-monopole in the multi-instanton solution is studied in the Polyakov-like gauge, where $A_4(x)$ is diagonalized. The world line of the QCD-monopole is found to be penetrate the center of each instanton. For the single-instanton solution, the QCD-monopole trajectory becomes a simple straight line. On the other hand, in the multi-instanton system, the QCD-monopole trajectory often has complicated topology including a loop or a folded structure, and is unstable against a small fluctuation of the location and the size of instantons. We also study the thermal instanton system in the Polyakov-like gauge. At the high-temperature limit, the monopole trajectory becomes straight lines in the temporal direction. The topology of the QCD-monopole trajectory is drastically changed at a high temperature.