Study of topological configurations playing the dominant role for quark confinement

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We have established the analytical and numerical method for finding in a gauge-invariant manner magnetic monopoles which are indispensable for the dual superconductivity for understanding quark confinement, and have obtained new findings on magnetic monopole in the Yang-Mills theory. Although it was believed that instantons in the Yang-Mills theory do not contribute to quark confinement, we have discovered that a circular loop of magnetic monopole is generated from the 2-instanton of Jackiw-Nohl-Rebbi type in four dimensional SU(2) Yang-Mills theory, and confirmed simultaneously the preceding results that 1-instanton and 2-instanton of the 'tHooft type obtained in a certain limit do not generate such a magnetic monopole. In SU(3) Yang-Mills theory, we have shown that non-Abelian U(2) magnetic monopoles plays the dominant role in confinement, in sharp contrast to the conventional Abelian projection.