  We critically reconsider the Landau-Ginzburg-Wilson (LGW) approach to
critical phenomena in the presence of gauge symmetries. In the LGW framework,
to obtain the universal features of a continuous transition, one identifies the
order parameter Phi and considers the corresponding most general Phi4 field
theory that has the same symmetries as the original model. In the presence of
gauge symmetries, one usually considers a gauge-invariant order parameter and a
LGW field theory that is invariant under the global symmetries of the original
model. We show that this approach, in which the gauge dynamics is effectively
integrated out, may sometimes lead to erroneous conclusions on the nature of
the critical behavior. As an explicit example, we show that the above-described
LGW approach generally fails for the three-dimensional ferromagnetic and
antiferromagnetic CP(N-1) models, which are invariant under global U(N) and
local U(1) transformations. We point out possible implications for the
finite-temperature chiral transition of nuclear matter.
