  Topological matter is characterized by the presence of a topological BF term
in its long-distance effective action. Topological defects due to the
compactness of the U(1) gauge fields induce quantum phase transitions between
topological insulators, topological superconductors and topological
confinement. In conventional superconductivity, due to spontaneous symmetry
breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In
this paper we derive the corresponding effective actions for the
electromagnetic field in topological superconductors and topological
confinement phases. In topological superconductors magnetic flux is confined
and the photon acquires a topological mass through the BF mechanism: no
symmetry breaking is involved, the ground state has topological order and the
transition is induced by quantum fluctuations. In topological confinement,
instead, electric charge is linearly confined and the photon becomes a massive
antisymmetric tensor via the St\"uckelberg mechanism. Oblique confinement
phases arise when the string condensate carries both magnetic and electric flux
(dyonic strings). Such phases are characterized by a vortex quantum Hall effect
potentially relevant for the dissipationless transport of information stored on
vortices.
