  We study Quantum Electrodynamics in d=3 (QED_3) coupled to N_f flavors of
fermions. The theory flows to an IR fixed point for N_f larger than some
critical number N_f^c. For N_f<= N_f^c, chiral-symmetry breaking is believed to
take place. In analogy with the Wilson-Fisher description of the critical O(N)
models in d=3, we make use of the existence of a perturbative fixed point in
d=4-2epsilon to study the three-dimensional conformal theory. We compute in
perturbation theory the IR dimensions of fermion bilinear and quadrilinear
operators. For small N_f, a quadrilinear operator can become relevant in the IR
and destabilize the fixed point. Therefore, the epsilon-expansion can be used
to estimate N_f^c. An interesting novelty compared to the O(N) models is that
the theory in d=3 has an enhanced symmetry due to the structure of 3d spinors.
We identify the operators in d=4-2epsilon that correspond to the additional
conserved currents at d=3 and compute their infrared dimensions.
