Lattice Study of $U_A(1)$ Anomaly: The Role of QCD-Monopoles

We investigate the role of QCD-monopoles for the $U_A(1)$ anomaly in the maximally abelian gauge within the SU(2) lattice gauge theory. The existence of the strong correlation between instantons and QCD-monopoles in the abelian gauge was already shown by both analytic and numerical works including the Monte Carlo simulation. Their interrelation brings us a conjecture that the presence of QCD-monopoles plays a considerable role on the $U_A(1)$ anomaly. We find an evidence for our conjecture on a determination of the fermionic zero modes of the Dirac operator in both the monopole removed'' gauge configuration and the photon removed’’ gauge configuration.