Chiral symmetry breaking, instantons, and monopoles

The purpose of this study is to show that monopoles induce the chiral symmetry breaking. In order to indicate the evidence, we add one pair of monopoles with magnetic charges to the quenched SU(3) configurations by a monopole creation operator, and investigate the propaties of the chiral symmetry breaking using the Overlap fermion. We show that instantons are created by the monopoles. The pseudoscalar meson mass and decay constant are computed from the correlation functions, and the renormalization constant $Z_{S}$ is determined by the non perturbative method. The renormalization group invariant chiral condensate in $\overline{\mbox{MS}}$-scheme at 2 [GeV] is evaluated by the Gell-Mann-Oakes-Renner formula, and the random matrix theory. Finally, we estimate the renormalization group invariant quark masses $\bar{m} = (m_{u} + m_{d})/2$, and $m_{s}$ in $\overline{\mbox{MS}}$-scheme at 2 [GeV]. The preliminary results indicate that the chiral condensate decreases and the quark masses become slightly heavy by increasing the number of monopole charges.

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