Introducing vortices in the continuum using direct and indirect methods

Abstract

Inspired by direct and indirect maximal center gauge methods which confirm the existence of vortices in lattice calculations and by using the connection formalism, we show that under some appropriate gauge transformations vortices and chains appear in the QCD vacuum of the continuum limit. In the direct method, by applying center gauge transformation and \textquotedblleft center projection,\textquotedblright QCD is reduced to a gauge theory including vortices, which corresponds to the non-trivial first homotopy group ${\Pi }_1\left(\text{SO}(3)\right)=Z_2.$ On the other hand, using the indirect method, in addition to the center gauge transformation and \textquotedblleft center projection,\textquotedblright an initial step called Abelian gauge transformation and then Abelian projection are applied. Therefore, instead of single vortices, chains that contain monopoles and vortices appear in the theory.

16 pages, 8 figures

References in corpus (4)

• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• Reformulating SU(N) Yang-Mills theory based on change of variables
• Magnetic monopoles and center vortices as gauge-invariant topological defects simultaneously responsible for confinement
• Contributions of the center vortices and vacuum domain in potentials between static sources

Cited by in corpus (1)

• Monopoles, vortices and their correlations in SU(3) gauge group