U_A(1) Anomaly in Background Fields Dominated by QCD-Monopoles on SU(2) Lattice

We study $U_A$(1) anomaly of non-perturbative QCD in the maximally abelian gauge on SU(2) lattice. The existence of the strong correlation between QCD-monopoles and instantons in the abelian gauge is shown by both analytic and numerical works including lattice simulations. These results bring us a conjecture that the $U_A$(1) symmetry would be explicitly broken in the background fields dominated by QCD-monopoles. We find an evidence for our conjecture by measuring the chiral-asymmetric zero modes of the Dirac operator in the backgrounds of QCD-monopoles.