Chern–Simons and WZW anomaly cancelations across dimensions

The WZW functional in D=4D=4 can be derived directly from the Chern–Simons functional of a compactified D=5D=5 gauge theory and the boundary fermions it supplants. A simple pedagogical model based on U(1)U(1) gauge groups illustrates how this works. A bulk-boundary system with the fermions eliminated manifestly evinces anomaly cancelations between CS and WZW terms.