Correlation between confinement and chiral-symmetry breaking in the dual Higgs theory

We study the correlation between confinement and dynamical chiral-symmetry breaking $\left(\mathrm{D}\mathrm{\chi }\mathrm{}\mathrm{SB}\right)$ in the dual Ginzburg-Landau (DGL) theory using the effective potential formalism. The DGL theory is an infrared effective theory based on the dual Higgs mechanism, and provides the nonperturbative gluon propagator, which leads to the linear quark potential. The screening effect for the confining potential can be obtained by introducing the infrared cutoff corresponding to the hadron size. We formulate the effective potential for $\mathrm{D}\mathrm{\chi }\mathrm{}\mathrm{SB}$ in the DGL theory, and find the vacuum instability against quark condensation. To extract the confinement effect, we separate the effective potential into the confinement part and others by dividing the confinement term from other terms in the gluon propagator in the DGL theory. The confinement part provides the dominant contribution to $\mathrm{D}\mathrm{\chi }\mathrm{}\mathrm{SB}$, which is regarded as monopole dominance for $\mathrm{D}\mathrm{\chi }\mathrm{}\mathrm{SB}$. The relevant energy for $\mathrm{D}\mathrm{\chi }\mathrm{}\mathrm{SB}$ is found to be the infrared region below 1 GeV. Monopole dominance for the DGL propagator is also found in the intermediate region 0.2 fm $\lesssim r\lesssim 1$ fm.