A new example of N=2 supersymmetric Landau-Ginzburg theories: the two-ring case

TL;DR

This paper presents a novel N=2 supersymmetric Landau-Ginzburg theory with a two-ring critical value configuration, demonstrating that its vacuum state metric obeys a non-Abelian 2x2 Toda system under specific deformations.

Contribution

It introduces a new example of Landau-Ginzburg theories with a two-ring critical value structure and links its vacuum metric to a non-Abelian Toda system.

Findings

Vacuum state metric satisfies non-Abelian 2x2 Toda equations.

Deformations preserving the two-ring configuration do not alter the form of the metric.

Provides a new integrable structure in supersymmetric Landau-Ginzburg models.

Abstract

The new example of N=2 supersymmetric Landau-Ginzburg theories is considered when the critical values of the superpotential w(x) form the regular two-ring configuration. It is shown that at the deformation, which does not change the form of this configuration, the vacuum state metric satisfies the equation of non-Abelian 2 x 2 Toda system.