Coarse separation and splittings in right-angled Artin groups

In this article, we characterise geometrically when a right-angled Artin group splits over an abelian subgroup. More precisely, given a finite graph $\mathrm{\Gamma }$, we show that $A(\mathrm{\Gamma })$ splits over an abelian subgroup if and only if it is coarsely separable by a family of subexponential growth, which amounts to saying that $\mathrm{\Gamma }$ is complete or separated by a complete subgraph.