  We investigate the continuum limit of a compact formulation of the lattice
U(1) gauge theory in 4 dimensions using a nonperturbative gauge-fixed
regularization. We find clear evidence of a continuous phase transition in the
pure gauge theory for all values of the gauge coupling (with gauge symmetry
restored). When probed with quenched staggered fermions with U(1) charge, the
theory clearly has a chiral transition for large gauge couplings. We identify
the only possible region in the parameter space where a continuum limit with
nonperturbative physics may appear.
