  Using accurate first-principles calculations based on many-body perturbation
theory we predict that two-dimensional MoS$_2$ hosts edge excitons with
universal character, intrinsic to the existence of edges and lying well below
the onset of bulk features. These excitons are largely insensitive to edge
terminations or orientation, persisting even in the presence of metallic
screening at zigzag edges, with large binding energies of $\sim$0.4 eV.
Additional excitons can also emerge in ultranarrow ribbons, or as a function of
the chemical nature of the termination. The chemical, structural, and
electronic similarities with Se- or W-based transition-metal dichalcogenides
suggest that these optical features could be common in this class of materials.
