Magnetic superconductivity and a linear response theory for non-Abelian gauge fields

We investigate properties of magnetic superconductivity as a mechanism for quark confinement. There are two kinds of magnetic permeability, ${\mu }^{\mathrm{ele}}$ and ${\mu }^{\mathrm{mag}}$, in non-Abelian gauge theory. Necessary conditions for electric and magnetic superconductivity are given by ${\mu }^{\mathrm{ele}}\sim 0$ and ${\mu }^{\mathrm{mag}}\sim 0$, respectively. Employing a linear response theory, we find that ${\mu }^{\mathrm{mag}}$ is related to a two-point correlation function of field strengths and that the condition ${\mu }^{\mathrm{mag}}\sim 0$ can be satisfied in non-Abelian gauge theory.