  We study in detail the properties of pi-fluxes embedded in a state with a
finite density of anyons that form either a Fermi liquid or a Bose-Einstein
condensate. By employing a recently developed exact lattice bosonization in 2D,
we demonstrate that such pi-flux remains a fully deconfined quasiparticle with
a finite energy cost in a Fermi liquid of emergent fermions coupled to a Z2
gauge field. This pi-flux is accompanied by a screening cloud of fermions,
which in the case of a Fermi gas with a parabolic dispersion binds exactly 1/8
of a fermionic hole. In addition there is a long-ranged power-law oscillatory
disturbance of the liquid surrounding the pi-flux akin to Friedel oscillations.
These results carry over directly to the pi-flux excitations in orthogonal
metals. In sharp contrast, when the pi-flux is surrounded by a Bose-Einstein
condensate of particles coupled to a Z2 gauge field, it binds a superfluid
half-vortex, becoming a marginally confined excitation with a logarithmic
energy cost divergence.
