English

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

Mathematical Physics 2024-10-31 v1 math.MP Exactly Solvable and Integrable Systems

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 AnA_n- and BnB_n-type multi-parameter rational solutions, relating them to known and new trigonometric solutions.

Keywords

Cite

@article{arxiv.2407.20349,
  title  = {Legendre transforms for type $A_{n}$ and $B_{n}$ $\vee$-systems},
  author = {Misha Feigin and Leo Kaminski and Ian A. B. Strachan},
  journal= {arXiv preprint arXiv:2407.20349},
  year   = {2024}
}

Comments

28 pages

R2 v1 2026-06-28T17:57:28.102Z