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We have presented non-Abelian dual superconductivity picture in the SU(3) Yang-Mills(YM) theory, and shown evidences such as the restricted U(2)-field dominance and the non-Abelian magnetic monopole dominance in the string tension. To establish the dual superconductivity picture, the dual Meissner effect in Yang-Mills theory must be examined, and we also presented the evidence of non-Abelian dual Meissner effect by measuring chromo-electric flux tube in the last lattice conferences. In this talk, by applying a new formulation of the YM theory on a lattice, the we further investigate the nonAbelian dual Meissner effect for SU(3) YM theory through correlation function. We examine non-abelian magnetic monopole currents as well as color flux created by the quark-antiquark source.

Gluon propagators in the deep IR region and non-Abelian dual superconductivity for SU(3) Yang-Mills theory