  We present an electrostatic theory of band gap renormalization in
atomically-thin semiconductors that captures the strong sensitivity to the
surrounding dielectric environment. In particular, our theory aims to correct
known band gaps, such as that of the three-dimensional bulk crystal. Combining
our quasiparticle band gaps with an effective mass theory of excitons yields
environmentally-sensitive optical gaps as would be observed in absorption or
photoluminescence. For an isolated monolayer of MoS$_2$, the presented theory
is in good agreement with ab initio results based on the GW approximation and
the Bethe-Salpeter equation. We find that changes in the electronic band gap
are almost exactly offset by changes in the exciton binding energy, such that
the energy of the first optical transition is nearly independent of the
electrostatic environment, rationalizing experimental observations.
