  We study a system of nanowires, i.e., the theory of 1+1 dimensional massless
fermions interacting with 3+1 dimensional U(1) gauge fields. When allowing for
non-zero chemical potentials, this system has a complex action problem in the
conventional formulation. We show that the partition sum can be mapped to a
dual representation where the fermions correspond to dimers and oriented loops
on 2-dimensional planes embedded in 4 dimensions. The dual degrees of freedom
for the gauge fields are surfaces that either are closed or bounded by the
fermion loops. In terms of the dual variables the complex action problem is
overcome and Monte Carlo simulations are possible for arbitrary chemical
potentials.
