Abstract
We analytically study the critical phase of a mixed system of the U(2) gauge fields and global symmetry on the boundary using gauge/gravity. A variational minimization problem has been formulated. The numerical results pertinently show that there exists a minimum chemical potential in which both scalar (s-wave) and vector (p-wave) condensates exist in a mixture, as well as in the distinct s- and p-phases. This result is obtained by breaking the symmetry into U(1) symmetry and rotational symmetry. While the analytical solutions of condensates and charge densities are achieved in both cases: the balanced and unbalanced holographic superconductors. This is the first analytical study of the coexistence of two modes of the superconductivity with different order parameters. The realistic model consists of two different phases of the superfluidity in helium.