  We study theoretically the collective dynamics of rotational excitations of
polar molecules loaded into an optical lattice in two dimensions. These
excitations behave as hard-core bosons with a relativistic energy dispersion
arising from the dipolar coupling between molecules. This has interesting
consequences for the collective many-body phases. The rotational excitations
can form a Bose-Einstein condensate at non-zero temperature, manifesting itself
as a divergent $T_2$ coherence time of the rotational transition even in the
presence of inhomogeneous broadening. The dynamical evolution of a dense gas of
rotational excitations shows regimes of non-ergodicity, characteristic of
many-body localization and localization protected quantum order.
