Integrable sigma models with Haantjes structure on ${H_{4}}$ Lie group

TL;DR

This paper classifies algebraic Haantjes structures on the ${h_{4}}$ Lie algebra, deforms a sigma model using these structures, and identifies three new integrable models on the ${H_{4}}$ Lie group.

Contribution

It provides a complete classification of algebraic Haantjes structures on ${h_{4}}$ and constructs three novel integrable sigma models utilizing these structures.

Findings

34 inequivalent algebraic Haantjes structures on ${h_{4}}$

Conditions for integrability of deformed sigma models derived

Three new integrable sigma models on ${H_{4}}$ obtained

Abstract

By solving algebraic relations for the conditions of Haantjes structure on a Lie algebra ${\G}$ and by using the corresponding automorphism group we proceed to classify all inequivalent algebraic Haantjes structures on ${\G}$. In this manner, we obtain 34 inequivalent algebraic Haantjes structures on the ${h_{4}}$ Lie algebra. We deform the chiral sigma model on a Lie group by using Haantjes structure on it. Then we try to obtain conditions on this structure such that the deformed sigma model remains to be integrable. Finally, using the ${h_{4}}$ Haantjes structures and solving this conditions three new integrable sigma models on the ${H_{4}}$ Lie group are obtained.