The E-expansion for QED

We study Quantum Electrodynamics in d = 3 (QED₃) coupled to Nf 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 use the existence of a fixed point in d = 4-2E to study the three-dimensional theory. We show how the E-expansion can be used to study the anomalous dimension of 2-and 4-fermion operators. The latter leads to an estimate of the critical number N_f^c. An important novelty compared to the O(N) models is that, because of the structure of spinors, the theory in d = 3 has an enhanced symmetry. We identify the operators in d = 4-2E that correspond to the additional conserved currents at d = 3.