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We consider relativistic U(1) gauge theories in 2+1 dimensions, with N_bspecies of complex bosons and N_f species of Dirac fermions at finitetemperature. The quantum phase transition between the Higgs and Coulomb phasesis described by a conformal field theory (CFT). At large N_b and N_f, but forarbitrary values of the ratio N_b/N_f, we present computations of variouscritical exponents and universal amplitudes for these CFTs. We make contactwith the different spin-liquids, charge-liquids and deconfined critical pointsof quantum magnets that these field theories describe. We compute physicalobservables that may be measured in experiments or numerical simulations ofinsulating and doped quantum magnets.

Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions