Singularity Theory for W-Algebra Potentials

TL;DR

This paper applies algebraic-geometric methods to analyze the singularities and phase structure of Landau potentials in W3-algebra models, revealing their ground states and perturbations.

Contribution

It introduces a novel algebraic-geometric approach to analyze W3-algebra Landau potentials and identifies their singularities and phase structures.

Findings

Number of ground states equals number of independent perturbations.

Singularities of the potentials are explicitly identified.

The structure of ground states matches previous IRF model results.

Abstract

The Landau potentials of $W_3$-algebra models are analyzed with algebraic-geometric methods. The number of ground states and the number of independent perturbations of every potential coincide and can be computed. This number agrees with the structure of ground states obtained in a previous paper, namely, as the phase structure of the IRF models of Jimbo et al. The singularities associated to these potentials are identified.