  We address the properties of excitons in monolayer MoS$_2$ from a theoretical
point of view, showing that low-energy excitonic states occur both at the
Brillouin zone center and at the Brillouin-zone corners, that binding energies
at the Brillouin-zone center deviate strongly from the $(n-1/2)^{-2}$ pattern
of the two-dimensional hydrogenic model, and that the valley-degenerate exciton
doublet at the Brillouin-zone center splits at finite momentum into an upper
mode with non-analytic linear dispersion and a lower mode with quadratic
dispersion. Although monolayer MoS$_2$ is a direct-gap semiconductor when
classified by its quasiparticle band structure, it may well be an indirect gap
material when classified by its excitation spectra.
