  The vacuum structure and spectra of two-dimensional gauge theories with
N=(2,2) supersymmetry are investigated. These theories admit a twisted mass
term for charged chiral matter multiplets. In the case of a U(1) gauge theory
with N chiral multiplets of equal charge, an exact description of the BPS
spectrum is obtained for all values of the twisted masses. The BPS spectrum has
two dual descriptions which apply in the Higgs and Coulomb phases of the theory
respectively. The two descriptions are related by a massive analog of mirror
symmetry: the exact mass formula which is given by a one-loop calculation in
the Coulomb phase gives predictions for an infinite series of instanton
corrections in the Higgs phase. The theory is shown to exhibit many phenomena
which are usually associated with N=2 theories in four dimensions. These
include BPS-saturated dyons which carry both topological and Noether charges,
non-trivial monodromies of the spectrum in the complex parameter space, curves
of marginal stability on which BPS states can decay and strongly coupled vacua
with massless solitons and dyons.
