Lagrangians for the W-Algebra Models

TL;DR

This paper derives simple polynomial Lagrangians for minimal W-algebra models, enabling phase diagram analysis and revealing connections to IRF models through specific perturbations.

Contribution

It provides a polynomial algebra description of W-algebra minimal models and constructs their Landau-Ginzburg Lagrangians, linking phase structures to IRF models.

Findings

Complete Landau-Ginzburg Lagrangians for W-algebra models

Identification of perturbations matching IRF model phase diagrams

Description of phase diagrams with $D_n$ symmetry

Abstract

The field algebra of the minimal models of W-algebras is amenable to a very simple description as a polynomial algebra generated by few elementary fields, corresponding to order parameters. Using this description, the complete Landau-Ginzburg lagrangians for these models are obtained. Perturbing these lagrangians we can explore their phase diagrams, which correspond to multicritical points with $D_n$ symmetry. In particular, it is shown that there is a perturbation for which the phase structure coincides with that of the IRF models of Jimbo et al.