The Inversion Symmetry of the WDVV Equations and Tau Functions

Si-Qi Liu; Dingdian Xu; Youjin Zhang

The Inversion Symmetry of the WDVV Equations and Tau Functions

Differential Geometry 2013-05-07 v2 Exactly Solvable and Integrable Systems

Authors: Si-Qi Liu , Dingdian Xu , Youjin Zhang

Abstract

For two solutions of the WDVV equations that are related by the inversion symmetry, we show that the associated principal hierarchies of integrable systems are related by a reciprocal transformation, and the tau functions of the hierarchies are related by a Legendre type transformation. We also consider relationships between the Virasoro constraints and the topological deformations of the principal hierarchies.

Keywords

WDVV equations inversion symmetry principal hierarchies reciprocal transformation tau functions Legendre transformation Virasoro constraints topological deformations

Cite

@article{arxiv.1012.5708,
  title  = {The Inversion Symmetry of the WDVV Equations and Tau Functions},
  author = {Si-Qi Liu and Dingdian Xu and Youjin Zhang},
  journal= {arXiv preprint arXiv:1012.5708},
  year   = {2013}
}

Comments

28 pages. This is a rewritten of an early preprint arXiv: 1002.0034 with a proof of Conjecture 6.1. V2: The published version

The Inversion Symmetry of the WDVV Equations and Tau Functions

Abstract

Keywords

Cite

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