The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms

The vacuum structure and spectra of two-dimensional gauge theories withN=(2,2) supersymmetry are investigated. These theories admit a twisted massterm for charged chiral matter multiplets. In the case of a U(1) gauge theorywith N chiral multiplets of equal charge, an exact description of the BPSspectrum is obtained for all values of the twisted masses. The BPS spectrum hastwo dual descriptions which apply in the Higgs and Coulomb phases of the theoryrespectively. The two descriptions are related by a massive analog of mirrorsymmetry: the exact mass formula which is given by a one-loop calculation inthe Coulomb phase gives predictions for an infinite series of instantoncorrections in the Higgs phase. The theory is shown to exhibit many phenomenawhich are usually associated with N=2 theories in four dimensions. Theseinclude BPS-saturated dyons which carry both topological and Noether charges,non-trivial monodromies of the spectrum in the complex parameter space, curvesof marginal stability on which BPS states can decay and strongly coupled vacuawith massless solitons and dyons.Comment: 51 page, LaTeX, Typos correcte