Flavor and topological current correlators in parity-invariant three-dimensional QED

We use lattice regularization to study the flow of the flavor-triplet fermion current central charge $C^f_J$ from its free field value in the ultraviolet limit to its conformal value in the infrared limit of the parity-invariant three-dimensional QED with two flavors of two-component fermions. The dependence of $C^f_J$ on the scale is weak with a tendency to be below the free field value at intermediate distances. Our numerical data suggests that the flavor-triplet fermion current and the topological current correlators become degenerate within numerical errors in the infra-red limit, thereby supporting an enhanced O(4) symmetry predicted by strong self-duality. Further, we demonstrate that fermion dynamics is necessary for the scale-invariant behavior of parity-invariant three-dimensional QED by showing that the pure gauge theory with non-compact gauge action has non-zero bilinear condensate.