Landau-Ginzburg-Wilson approach to critical phenomena in the presence of gauge symmetries

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 Φ and considers the corresponding most general Φ4 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 CPN-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