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

Mirenayatollah Bahadori; Ali Eghbali; Adel Rezaei-Aghdam

doi:10.1016/j.nuclphysb.2026.117491

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arXiv · 2605.20851

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

Mirenayatollah Bahadori·Ali Eghbali·Adel Rezaei-Aghdam

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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.

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Mirenayatollah Bahadori, Ali Eghbali, Adel Rezaei-Aghdam. 2026-05-20. Integrable sigma models with Haantjes structure on ${H_{4}}$ Lie group. https://doi.org/10.1016/j.nuclphysb.2026.117491

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