  Z3 gauge theory with dynamical (bosonic) matter is studied in 4 dimensions
with a finite chemical potential. This theory could be viewed as an effective
theory describing the centre vortex picture of QCD colour confinement, but it
is studied here with local interactions as theory in its own right. It is shown
that the sign-problem can be solved by dualisation. The dual theory is derived:
the pure gauge sector is a theory of closed membranes with Nambu-Goto action,
and matter is described by open branes bounded by closed matter loops. The
brane theory is simulated with Monte-Carlo techniques. Some evidence is found
that the theory possesses a weakly-renormalisable phase with the scale set by a
mass gap. Deconfinement at low temperatures and finite chemical potentials
appears as a percolation transition for matter loops.
