Chiral QED out of matter

In a previous paper we have shown how the Wilsonian renormalization group naturally leads to the equivalence of the standard QED with a matter-only theory. In this paper we give an improved explanation of the equivalence and discuss, as an example, the equivalence of a chiral QED in the Higgs phase with a matter-only theory. Ignoring the contributions suppressed by the negative powers of a UV cutoff, the matter-only theory is equivalent to the perturbatively renormalizable chiral QED with two complex Higgs fields. In the matter-only theory chiral anomaly arises without elementary gauge fields.