  We study N=(2,2) supersymmetric abelian gauge theories in two dimensions. The
exact BPS spectrum of these models is shown to coincide with the spectrum of
massive hypermultiplets of certain N=2 supersymmetric gauge theories in four
dimensions. A special case of these results involves a surprising connection
between four-dimensional N=2 SQCD with N colours and N_{f}>N flavours at the
root of the baryonic Higgs branch and the supersymmetric CP^{2N-N_{f}-1}
sigma-model in two dimensions. This correspondence implies a new prediction for
the strong-coupling spectrum of the four-dimensional theory.
