Phase structure of SU(2) Yang-Mills theory with global center symmetry

Retaining only the ‘timelike’ component A0 of the vector potential a skelet model with explicit global center symmetry is constructed for SU(2) Yang-Mills theory. It is shown that the A0 gluon vacuum is equivalent with the 4-dimensional Coulomb-gas. In 1–loop approximation, the effective theory of the skelet model exhibits non-local self-interaction. A coupling constant λ is found that governs the loop expansion. For λ < 1 the effective theory does not confine (the string tension vanishes), whereas for λ = 1 confinement (with non-vanishing string tension) takes place. In the deconfined phase the A0 gluons exhibit non-zero rest mass and global center symmetry is broken by the vacuum state. Confinement sets on for λ = 1 when the rest mass of A0 gluons vanishes and the global center symmetry of the vacuum is restored. PACS number(s): 11.15.Tk, 11.10.Lm