Generalized Legendre transformations and symmetries of the WDVV equations

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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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
608951Engineering and Physical Sciences Doctoral Training Grant 2012-16Mary Beth KneafseyEngineering & Physical Sciences Research Council (EPSRC)EP/K503058/1VPO VICE PRINCIPAL RESEARCH & ENTERPRISE