Holographic Model for Color Superconductivity in $${d}$$-Dimension Bulk without Confinement Phase

We generalize the concept of holography for the color superconductivity (CSC) phase by considering $$d$$ -dimensional Anti de Sitter (AdS) space instead of the traditional 6 dimensions. The corresponding dual field theory is a gauge theory with $$SU$$ ( $$N_{c}$$ ) symmetry defined in ( $$d-1$$ )-dimensions that, despite lacking a confinement phase, retains characteristics consistent with quantum chromodynamics (QCD) CSC. We then use a holographic model based on Einstein–Maxwell gravity and the standard Maxwell interaction in $$d$$ -dimensional AdS space to investigate this phenomenon for the number of colors $$N_{c}\geq 2$$ without confinement phase, identifying the dimensions where the model remains valid for $$N_{c}=2$$ .