On the integrability of N=2 Landau-Ginzburg models: A graph generalization of the Yang-Baxter equation

TL;DR

This paper explores the integrability of N=2 Landau-Ginzburg models through a novel graph-based Yang-Baxter equation, revealing solutions connected to the Chiral-Potts model's Boltzmann weights.

Contribution

It introduces a graph generalization of the Yang-Baxter equation and finds a non-trivial solution related to the Chiral-Potts model for specific perturbations.

Findings

A new graph-based Yang-Baxter equation is formulated.

A non-trivial solution linked to the Chiral-Potts model is discovered.

The solution applies to the $t_2$ perturbation of A-models.

Abstract

The study of the integrability properties of the N=2 Landau- Ginzburg models leads naturally to a graph generalization of the Yang-Baxter equation which synthetizes the well known vertex and RSOS Yang-Baxter equations. A non trivial solution of this equation is found for the $t_2$ perturbation of the A-models, which turns out to be intimately related to the Boltzmann weights of a Chiral- Potts model.