  We consider gauged sigma-models from a Riemann surface into a Kaehler and
hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted
to produce a gauged A-model. This model localizes to the moduli space of
solutions of the vortex equations and computes the Hamiltonian Gromov-Witten
invariants. When the target is equivariantly Calabi-Yau, i.e. when its first
G-equivariant Chern class vanishes, the supersymmetric theory can also be
twisted into a gauged B-model. This model localizes to the Kaehler quotient
X//G.
