Three new integrable models found by classifying geometric structures

Integrable systems—ones that can be solved exactly—are rare and prized in physics. The authors classified all distinct geometric structures (called Haantjes structures) on the h₄ Lie algebra, finding 34 inequivalent ones. They then deformed a standard quantum field model using these structures and derived conditions under which integrability survives. Three new integrable sigma models emerged as a result.