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. We point out that the generated gluon mass can cure the instability of the Savvidy vacuum. In fact, such a novel type of magnetic condensation is shown to occur by calculating the effective potential. 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. Finally, we discuss the implication to the Faddeev-Skyrme model with knot soliton as a low-energy effective theory of Yang-Mills theory.