Remark on the Emergence of Color Superconductivity for Gauge Theories in General Spacetime Dimensions from simple Holographic Models

TL;DR

This paper extends holographic models to arbitrary spacetime dimensions to analyze color superconductivity in confining gauge theories, revealing how dimensionality influences the CSC phase and phase transitions.

Contribution

It generalizes holographic models of color superconductivity to arbitrary dimensions, exploring phase transitions and CSC conditions in various spacetime settings.

Findings

CSC phase depends on spacetime dimension

Confinement-deconfinement transition analyzed holographically

Conditions for N_c=2 CSC in 4D case identified

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 an arbitrary confining gauge theory with $SU(N_c)$ symmetry, like quantum chromodynamics (QCD) CSC. We then use a holographic model based on Einstein-Maxwell gravity in $d$-dimensional AdS spacetime to study this phenomenon in both confinement and deconfinement phase, study the confinement$-$deconfinement phase transition and the condition for the $N_c=2$ CSC phase with $d=4$ case, one special case from arXiv:2411.05550