Non-Abelian strings in high-density QCD: Zero modes and interactions

The most fundamental strings in high-density color superconductivity are the non-Abelian semisuperfluid strings which have color-gauge flux tubes but behave as superfluid vortices in the energetic point of view. We show that in addition to the usual translational zero modes, these vortices have normalizable orientational zero modes in the internal space, associated with the color-flavor locking symmetry broken in the presence of the strings. The interaction among two parallel non-Abelian semisuperfluid strings is derived for general relative orientational zero modes to show the universal repulsion. This implies that the previously known superfluid vortices, formed by spontaneously broken U(1)B, are unstable to decay. Moreover, our result proves the stability of color superconductors in the presence of external color-gauge fields.