Trigonometric Solutions of the WDVV Equations from Root Systems
R. Martini, L.K. Hoevenaars
TL;DR
This paper constructs solutions to the WDVV equations of trigonometric type for all crystallographic root systems by introducing an extra variable and a Weyl invariant correction in five-dimensional Seiberg-Witten theory.
Contribution
It provides a systematic method to generate trigonometric solutions of the WDVV equations for all crystallographic root systems using a novel correction term.
Findings
Solutions applicable to all crystallographic root systems.
Extension of Seiberg-Witten theory with additional variables.
New class of trigonometric WDVV solutions.
Abstract
By introduction of an additional variable and addition of a Weyl invariant correction term to the perturbative prepotential in five-dimensional Seiberg-Witten theory we construct solutions of the WDVV equations of trigonometric type for all crystallographic root systems.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic and Geometric Analysis · Numerical methods for differential equations