  We consider rotating finite size vortex arrays in Bose-Einstein condensates
that are confined by cylindrically symmetric external potentials. We show that
such systems possess two exact Nambu-Goldstone zero modes associated with two
spontaneously broken continuous symmetries of the system. We verify our
analytical result via direct numerical diagonalizations of the Bogoliubov-de
Gennes equations. We conclude by comparing rotating vortex lattices in
superfluids to supersolids and discrete time crystals.
