  Abelian gauge theories formulated on a space-time lattice can be used as a
prototype for investigating the confinement mechanism. In U(1) lattice gauge
theory it is possible to perform a dual transformation of the path integral.
Simulating the obtained dual theory (which corresponds to a certain limit of a
dual Higgs model) including external sources, we perform a very accurate
analysis of flux tubes with respect to the dual superconductor picture. Dual
flux tube simulations are also performed in the full Abelian Higgs model, in
order to obtain non-perturbative control over quantum and string fluctuations,
and for a comparison to the results of dual QCD.
