  We consider relativistic U(1) gauge theories in 2+1 dimensions, with N_b
species of complex bosons and N_f species of Dirac fermions at finite
temperature. The quantum phase transition between the Higgs and Coulomb phases
is described by a conformal field theory (CFT). At large N_b and N_f, but for
arbitrary values of the ratio N_b/N_f, we present computations of various
critical exponents and universal amplitudes for these CFTs. We make contact
with the different spin-liquids, charge-liquids and deconfined critical points
of quantum magnets that these field theories describe. We compute physical
observables that may be measured in experiments or numerical simulations of
insulating and doped quantum magnets.
