The relationship between a topological Yang-Mills field and a magnetic monopole

We show that a Jackiw-Nohl-Rebbi solution, as the most general two-instanton, generates a circular loop of magnetic monopole in four-dimensional Euclidean SU(2) Yang-Mills theory.Comment: 3 pages, 2 figure; to be published in the proceedings of "BARYONS'10", Dec. 7-11, 2010, Osaka, Japa

Quark confinement due to non-Abelian magnetic monopoles in SU(3) Yang-Mills theory

We present recent results on quark confinement: in SU(3) Yang-Mills theory, confinement of fundamental quarks is obtained due to the dual Meissner effect originated from non-Abelian magnetic monopoles defined in a gauge-invariant way, which is distinct from the well-known Abelian projection scenario. This is achieved by using a non-Abelian Stokes theorem for the Wilson loop operator and a new reformulation of the Yang-Mills theory.Comment: 5 pages, 3 eps figures. Talk presented at QCD@Work 2012: International Workshop on QCD - Theory and Experiment, June 18-21, Lecce, Ital

Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory

The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the Yang-Mills theory based on change of variables extending the decomposition of the $SU(N)$ Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the $SU(N)$ Wilson loop operator. Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole.Comment: 304 pages; 62 figures and 13 tables; a version published in Physics Reports, including corrections of errors in v