  The 2-dimensional U(1) gauge-Higgs model with a topological term is a simple
example of a lattice field theory where the complex action problem comes from
the topological term. We show that the model can be exactly rewritten in terms
of dual variables, such that the dual partition sum has only real and positive
contributions. Using suitable algorithms the dual formulation allows for Monte
Carlo simulations at arbitrary values of the vacuum angle. We demonstrate the
feasibility of the dual simulation and study the continuum limit, as well as
the phase diagram of the system.
