  The U(1) gauge-Higgs model with two flavors of opposite charge and a chemical
potential is mapped exactly to a dual representation where matter fields
correspond to loops of flux and the gauge fields are represented by surfaces.
The complex action problem of the conventional formulation at finite chemical
potential mu is overcome in the dual representation and the partition sum has
only real and non-zero contributions. We simulate the model in the dual
representation using a generalized worm algorithm, explore the phase diagram
and study condensation phenomena at finite mu.
