A note on the Holographic model for color superconductivity in d-dimension without confinement phase

In this note, we will generalize the concept of the holography for the color superconductivity (CSC) phase becomes to d-dimension AdS instead of 6d. The dual field theory live in (d-1)-dimension $SU(N_c)$ and have no confinement phase contradiction with the QCD color superconductivity. And we will try to use holographic model with Einstein-Maxwell gravity in d dimension AdS and we study this phase with $N_c\ge 2$. And after, we will discuss the equation of state of the color superconductivity in $d=4$ case without confinement via holography