2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/16995A large variety of microscopic gauge theories can be written for antiferromagnetic spin systems, including $U(1), SU(2)$, and $Z_N$. I consider the question of the appropriate effective gauge theory for such systems. I show that while an SU(N) anti-ferromagnet can be written microscopically as a Z_N gauge theory, for unfrustrated systems, with a two-sublattice structure, there is always an effective U(1) gauge field. The dispersion relation for the gauge field is shown to depend on the presence or absence of charge-conjugation symmetry. Frustrated systems can break the gauge group to a discrete group, but this appears to always involve introducing a gap for the spinons.4 pages, references addedStrongly Correlated Electronstext