WDVV equations and invariant bi-Hamiltonian formalism

Abstract: The WDVV equations are central in Topological Field Theory and Integrable Systems. We prove that in low dimensions the WDVV equations are bi-Hamiltonian. The invariance of the bi-Hamiltonian formalism is proved for N = 3. More examples in higher dimensions show that the result might hold in general. The invariance group of the bi-Hamiltonian pairs is the group of projective reciprocal transformations. The significance of projective invariance of WDVV equations is discussed in detail. Computer algebra programs that were used for calculations throughout the paper are provided at github.com/Jakub-Vasicek/WDVV-computations/.

Based on a joint work with Jakub Vašíček.

mathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

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Geometry of differential equations seminar