Dual Higgs Mechanism based on the Dual Gauge Formalism in the Lattice QCD

We study the dual Higgs mechanism induced by monopole condensation based on the dual gauge formalism in the maximally abelian (MA) gauge in the lattice QCD. To examine ``monopole condensation'' in QCD, we study the monopole part or the monopole-current system appearing in the MA gauge by extracting the dual gluon field $B_\mu$. First, we investigate the inter-monopole potential using the dual Wilson loop in the lattice QCD simulation. In the monopole part in the MA gauge, the inter-monopole potential is found to be flat, and can be fitted as the Yukawa potential in the infrared region. From more detailed analysis of the inter-monopole potential considering the monopole size, we estimate the effective dual-gluon mass $m_B \simeq 0.5$GeV and the effective monopole size $R_{^{_{\rm M}}} \simeq 0.2$fm. Second, we study the dual gluon propagator $G^D_{\mu\nu}(x-y) \equiv < B_\mu(x) B_\nu(y) >_{\rm MA}$ in the MA gauge, and find that $G^D_{\mu\mu}$ behaves as the massive vector-boson propagator with $m_B \simeq 0.4$ GeV in the infrared region. The effective-mass acquirement of the dual gluon field $B_\mu$ at the long distance can be regarded as the lattice QCD evidence of ``infrared monopole condensation'' in the MA gauge.