  Vortices and vortex arrays have been used as a hallmark of superfluidity in
rotated, ultracold Fermi gases. These superfluids can be described in terms of
an effective field theory for a macroscopic wave function representing the
field of condensed pairs, analogous to the Ginzburg-Landau theory for
superconductors. Here, we have established how rotation modifies this effective
field theory, by rederiving it starting from the action of Fermi gas in the
rotating frame of reference. The rotation leads to the appearance of an
effective vector potential, and the coupling strength of this vector potential
to the macroscopic wave function depends on the interaction strength between
the fermions, due to a renormalization of the pair effective mass in the
effective field theory. The mass renormalization derived here is in agreement
with results of functional renormalization group theory. In the extreme BEC
regime, the pair effective mass tends to twice the fermion mass, in agreement
with the physical picture of a weakly interacting Bose gas of molecular pairs.
Then, we use our macroscopic wave function description to study vortices and
the critical rotation frequencies to form them. Equilibrium vortex state
diagrams are derived, and they are in good agreement with available results of
the Bogoliubov - De Gennes theory and with experimental data.
