  Exciton dispersion as a function of center-of-mass momentum, \textbf{Q}, is
essential to the understanding of exciton dynamics. We use the ab-initio
GW-Bethe Salpeter equation method to calculate the dispersion of excitons in
monolayer MoS$_2$ and find a nonanalytic light-like dispersion. This behavior
arises from an unusual $|Q|$ term in both the intra- and inter-valley exchange
of the electron-hole interaction, which concurrently gives rise to a valley
quantum phase of winding number two. A simple effective Hamiltonian to $Q^2$
order with analytic solutions is derived to describe quantitatively these
behaviors.
