Phases in holographic helical superconductor

We study SU(2)[Formula: see text]×[Formula: see text]U(1) gauge theory with Chern–Simons term, coupled to scalar field in adjoint, in a probe approximation by ignoring back reaction on metric. Considering a simple ansatz for non-Abelian gauge field with helical structure, we find it admits s-wave and p-wave phases along with their coexistence. We study free energies for different phases along with those for p-wave phases for different values of pitch and frequency dependence of optical conductivities below critical temperature.