Holographic Model for Color Superconductivity in \({d}\)-Dimension Bulk without Confinement Phase

Abstract

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 \(N_{c}=2\).