  A 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.
