Strachan, I. A.B. and Stedman, R. (2017) Generalized Legendre transformations and symmetries of the WDVV equations. Journal of Physics A: Mathematical and Theoretical, 50(9), 095202. (doi: 10.1088/1751-8121/aa58b2)
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Abstract
The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class - the so-called Legendre transformations - were introduced by Dubrovin. They are a discrete set of symmetries between the stronger concept of a Frobenius manifold, and are generated by certain flat vector fields. In this paper this construction is generalized to the case where the vector field (called here the Legendre field) is non-flat but satisfies a certain set of defining equations. One application of this more general theory is to generate the induced symmetry between almost-dual Frobenius manifolds whose underlying Frobenius manifolds are related by a Legendre transformation. This also provides a map between rational and trigonometric solutions of the WDVV equations.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Strachan, Professor Ian |
| Authors: | Strachan, I. A.B., and Stedman, R. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Physics A: Mathematical and Theoretical |
| Publisher: | IOP Publishing |
| ISSN: | 1751-8113 |
| ISSN (Online): | 1751-8121 |
| Published Online: | 27 January 2017 |
| Copyright Holders: | Copyright © 2017 IOP Publishing Ltd |
| First Published: | First published in Journal of Physics A: Mathematical and Theoretical 50(9): 095202 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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