Non-linear change of variables for the Yang-Mills theory: extracting gauge-invariant topological defects responsible for quark confinement
Seminar Room 1, Newton Institute
In order to understand quark confinement, we perform a non-linear change of variables for the gauge field to obtain a new formulation of Yang-Mills theory written in terms of new variables which was once known the Cho-Faddeev-Niemi-Shabanov decomposition. This reformulation is suggested from a non-Abelian Stokes theorem for the Wilson loop operator. The reformulation enables us to define a gauge-invariant magnetic monopole carrying the magnetic charge subject to the Dirac quantisation condition and to separate the "Abelian" and "magnetic monopole" components giving the dominant contribution to the string tension from the Wilson loop. In other words, this gives a gauge-invariant description of the dual superconductivity by recovering color symmetry and gauge covariance lost by the conventional Abelian projection method. Moreover, we have also constructed the lattice version to perform numerical simulations to confirm these statements. Finally, we discuss how the original Yang-Mills field configuration of instanton type is translated to the topological defects such as magnetic monopole and Hopfion in this reformulation in view of confinement.