As I understand it color confinement comes from the fact that as the distance between two color charges increases the color potential energy increases, instead of decreasing, and the energy needed to pull two quarks apart is the same as the energy needed to create two new quarks. The way the color potential energy between two color charges is related to the fact that gluons themselves have color charge. For the electric potential energy between two electric charges the relationship between distance and potential energy depends on the number of dimensions, and for the spacetime curvature around a massive body the relationship between the distance from the massive body and the spacetime curvature depends on the number of dimensions, but I'm not sure if the relationship between distance and color potential energy depends on the number of dimensions?
Would color confinement apply in $n+1$ dimensions, in which $n>3$, or could color charges be free particles in higher dimensions?
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