Landau-Ginzburg Lagrangians of minimal $W$-models with an integrable perturbation

TL;DR

This paper constructs Landau-Ginzburg Lagrangians for minimal bosonic $W$-models with an integrable perturbation, aligning with previous models and exploring soliton properties, suggesting a supersymmetric structure connection.

Contribution

It introduces Landau-Ginzburg Lagrangians for perturbed minimal bosonic $W$-models, extending previous unperturbed models and analyzing their soliton and algebraic properties.

Findings

Lagrangians agree with previous models for unperturbed cases

Perturbed models exhibit soliton structures similar to $N=2$ models

Properties like BPS solitons and $W$ plane lines are preserved

Abstract

We construct Landau-Ginzburg Lagrangians for minimal bosonic ($N=0$) $W$-models perturbed with the least relevant field, inspired by the theory of $N=2$ supersymmetric Landau-Ginzburg Lagrangians. They agree with the Lagrangians for unperturbed models previously found with Zamolodchikov's method. We briefly study their properties, e.g. the perturbation algebra and the soliton structure. We conclude that the known properties of $N=2$ solitons (BPS, lines in $W$ plane, etc.) hold as well. Hence, a connection with a generalized supersymmetric structure of minimal $W$-models is conjectured.