The BPS spectra of gauge theories in two and four dimensions

We study = (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 = 2 supersymmetric gauge theories in four dimensions. A special case of these results involves a surprising connection between four-dimensional = 2 SQCD with N colours and N$>Nf>N flavours at the root of the baryonic Higgs branch and the supersymmetric CP2N−Nf−1 σ-model in two dimensions. This correspondence implies a new prediction for the strong-coupling spectrum of the four-dimensional theory.