Topological configurations of Yang-Mills field responsible for magnetic-monopole loops as quark confiner

We have given a new description of the lattice Yang-Mills theory a la Cho-Faddeev-Niemi-Shabanov, which has enabled us to confirm in a gauge-independent manner "Abelian"-dominance and magnetic-monopole dominance in the Wilson loop average, yielding a gauge-independent dual superconductor picture for quark confinement. In particular, we have given a new procedure (called reduction) for obtaining a gauge-independent magnetic monopole from a given Yang-Mills field. In this talk, we demonstrate how some of known topological configurations in the SU(2) Yang-Mills theory such as merons and instantons generate closed loops of magnetic-monopole current as the quark confiner, both of which are characterized by the gauge-invariant topological index, topological charge (density) and magnetic charge (density), respectively. We also try to detect which type of topological configurations exist in the lattice data involving magnetic-monopole loops generated by Monte Carlo simulation. Here we apply a new geometrical algorithm based on "computational homology" to discriminating each closed loop from clusters of magnetic-monopole current, since the magnetic-monopole current on a lattice is integer valued.