  The physics of excitons, electron-hole pairs that are bound together by their
mutual Coulomb attraction, can to great extent be understood in the framework
of the quantum-mechanical hydrogen model. This model has recently been
challenged by spectroscopic measurements on two-dimensional transition-metal
dichalchogenides that unveil strong deviations from a hydrogenic spectrum.
Here, we show that this deviation is due to the particular relativistic
character of electrons in this class of materials. Indeed, their electrons are
no longer described in terms of a Schroedinger but a massive Dirac equation
that intimately links electrons to holes. Dirac excitons therefore inherit a
relativistic quantum spin-1/2 that contributes to the angular momentum and thus
the exciton spectrum. Most saliently, the level spacing is strongly reduced as
compared to the hydrogen model, in agreement with spectroscopic measurements
and ab-initio calculations.
