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arXiv · 2407.20349

Legendre transforms for type $A_{n}$ and $B_{n}$ $\vee$-systems

Misha Feigin·Leo Kaminski·Ian A. B. Strachan
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Abstract

The Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations have a rich structure related to the theory of Frobenius manifolds, with many known families of solutions. A Legendre transformation is a symmetry of the WDVV equations, introduced by Dubrovin. We explicitly compute the results of a Legendre transformation applied to $A_n$- and $B_n$-type multi-parameter rational solutions, relating them to known and new trigonometric solutions.

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Misha Feigin, Leo Kaminski, Ian A. B. Strachan. 2024-07-29. Legendre transforms for type $A_{n}$ and $B_{n}$ $\vee$-systems. https://doi.org/10.1088/1751-8121%2Fad8cb3

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