Abstract
The vacuum structure and spectra of two-dimensional gauge theories with
= (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 = 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.