Chiral symmetry breaking and monopoles

Abstract

To understand the relation between the chiral symmetry breaking and monopoles, the chiral con- densate which is the order parameter of the chiral symmetry breaking is calculated in the MS scheme at 2 [GeV]. First, we add one pair of monopoles, varying the monopole charges mc from zero to four, to SU(3) quenched configurations by a monopole creation operator. The low-lying eigenvalues of the Overlap Dirac operator are computed from the gauge links of the normal con- figurations and the configurations with additional monopoles. Next, we compare the distributions of the nearest-neighbor spacing of the low-lying eigenvalues with the prediction of the random matrix theory. The low-lying eigenvalues not depending on the scale parameter ∑ are compared to the prediction of the random matrix theory. The results show the consistency with the random matrix theory. Thus, the additional monopoles do not affect the low-lying eigenvalues. Moreover, we discover that the additional monopoles increase the scale parameter ∑. We then evaluate the chiral condensate in the MS scheme at 2 [GeV] from the scale parameter ∑ and the renormaliza-Tion constant Zs. The final results clearly show that the chiral condensate linearly decreases by increasing the monopole charges.