Possible second-order phase transition in strongly coupled unquenched planar four-dimensional QED

We study chiral-symmetry breaking in four-dimensional QED with N fermion species using truncated Schwinger-Dyson equations, and taking vacuum-polarization effects into account via a momentum-dependent gauge coupling. These effects transmute the infinite-order phase transition found previously for the case of a fixed gauge coupling into a second-order phase transition. For large N, the phase transition may not exist, as it is determined primarily by the physics at the cutoff. We also carry out a preliminary renormalization-group analysis of the theory near the critical coupling: the results are compatible with the existence of a nontrivial continuum limit for the planar theory at the critical value, with an effectively dimensionless fermion field.