Magnetic condensation , Abelian dominance , and instability of Savvidy vacuum

We show that a certain type of color magnetic condensation originating from magnetic monopole configurations is sufficient to provide the mass for off-diagonal gluons in the SU(2) Yang-Mills theory under the Cho–Faddeev– Niemi decomposition. In fact, such magnetic condensation is shown to occur by calculating the effective potential within the BRST quantization. This enables us to explain the infrared Abelian dominance and monopole dominance by way of a non-Abelian Stokes theorem, which suggests the dual superconductivity picture of quark confinement. We reexamine the instability of the Savvidy vacuum for the massive gluons. Finally, we discuss the implication to the Faddeev-Skyrme model with knot soliton as a low-energy effective theory of Yang-Mills theory.