Non-Abelian dual superconductor picture for quark confinement

Abstract

We give a theoretical framework for defining and extracting non-Abelian magnetic monopoles in a gauge-invariant way in $SU(N)$ Yang-Mills theory to study quark confinement. Then we give numerical evidences that the non-Abelian magnetic monopole defined in this way gives a dominant contribution to confinement of fundamental quarks in $SU(3)$ Yang-Mills theory, which is in sharp contrast to the $SU(2)$ case in which Abelian magnetic monopoles play the dominant role for quark confinement.