Chiral symmetry breaking and monopoles

TL;DR

This study investigates how adding monopoles to SU(3) gauge configurations affects chiral symmetry breaking, finding that monopoles increase the scale parameter but decrease the chiral condensate linearly.

Contribution

It demonstrates that monopoles influence the chiral condensate and confirms the consistency of low-lying eigenvalues with random matrix theory, providing new insights into monopole effects on chiral symmetry.

Findings

Monopoles do not affect low-lying eigenvalues' distribution.

Adding monopoles increases the scale parameter Σ.

Chiral condensate decreases linearly with monopole charge.

Abstract

To understand the relation between the chiral symmetry breaking and monopoles, the chiral condensate which is the order parameter of the chiral symmetry breaking is calculated in the $\overline{\mbox{MS}}$ scheme at 2 [GeV]. First, we add one pair of monopoles, varying the monopole charges $m_{c}$ 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 configurations 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 $\Sigma$ 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 $\Sigma$. We then evaluate the chiral condensate in the $\overline{\mbox{MS}}$ scheme at 2 [GeV] from the scale parameter $\Sigma$ and the renormalization constant $Z_{S}$. The final results clearly show that the chiral condensate linearly decreases by increasing the monopole charges.