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

## TL;DR

This paper critically examines the Landau-Ginzburg-Wilson approach to phase transitions with gauge symmetries, highlighting its limitations and providing examples where it fails, with potential implications for nuclear matter transitions.

## Contribution

The paper demonstrates that the standard LGW approach can be incorrect for certain gauge-invariant models, challenging its universal applicability in critical phenomena analysis.

## Key findings

- LGW approach may lead to incorrect conclusions in gauge symmetry contexts
- Fails for 3D CP(N-1) models with global U(N) and local U(1) symmetries
- Implications for understanding finite-temperature chiral transitions in nuclear matter

## Abstract

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.