  We introduce the notion of metrically systolic simplicial complexes. We study
geometric and large-scale properties of such complexes and of groups acting on
them geometrically. We show that all two-dimensional Artin groups act
geometrically on metrically systolic complexes. As direct corollaries we obtain
new results on two-dimensional Artin groups and all their finitely presented
subgroups: we prove that the Conjugacy Problem is solvable, and that the Dehn
function is quadratic. We also show several large-scale features of finitely
presented subgroups of two-dimensional Artin groups, lying background for
further studies concerning their quasi-isometric rigidity.
