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 $N_c = 2$.