The construction of Frobenius manifolds from KP tau-functions

Details The construction of Frobenius manifolds from KP tau-functions The construction of Frobenius manifolds from KP tau-functions

1998-08-18

arxiv.org/abs/solv-int/9808008v1

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, latex2e, no figures

Scientific paper

10.1007/s002200050691

Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux-Egoroff equations. This system of partial differential equations appears as a specific subset of the $n$-component KP hierarchy. KP representation theory and the related Sato infinite Grassmannian are used to construct solutions of this Darboux-Egoroff system and the related Frobenius manifolds. Finally we show that for these solutions Dubrovin's isomonodromy tau-function can be expressed in the KP tau-function.

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