Quantum electrodynamics in d=3 from the ϵ expansion

We study quantum electrodynamics in d=3 coupled to Nf flavors of fermions. The theory flows to an IR fixed point for Nf larger than some critical number Nfc. For Nf≤Nfc, 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 fixed point in d=4-2ϵ to study the three-dimensional conformal theory. We compute, in perturbation theory, the IR dimensions of fermion bilinear and quadrilinear operators. For small Nf, a quadrilinear operator can become relevant in the IR and destabilize the fixed point. Therefore, the epsilon expansion can be used to estimate Nfc. 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=4-2ϵ that correspond to the additional conserved currents at d=3 and compute their infrared dimensions.