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

Understand

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.