  We investigate the critical behavior of three-dimensional antiferromagnetic
CP(N-1) [ACP(N-1)] models in cubic lattices, which are characterized by a
global U(N) symmetry and a local U(1) gauge symmetry. Assuming that critical
fluctuations are associated with a staggered gauge-invariant (hermitian
traceless matrix) order parameter, we determine the corresponding
Landau-Ginzburg-Wilson (LGW) model. For N=3 this mapping allows us to conclude
that the three-component ACP(2) model undergoes a continuous transition that
belongs to the O(8) vector universality class, with an effective enlargement of
the symmetry at the critical point. This prediction is confirmed by a detailed
numerical comparison of finite-size data for the ACP(2) and the O(8) vector
models. We also present a renormalization-group (RG) analysis of the LGW
theories for N>3. We compute perturbative series in two different
renormalization schemes and analyze the corresponding RG flow. We do not find
stable fixed points that can be associated with continuous transitions.
