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Integrable Structure behind WDVV Equations

Henrik Aratyn·Johan van de Leur
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Abstract

An integrable structure behind Witten--Dijkgraaf--Verlinde--Verlinde (WDVV) equations is identified with reduction of a Riemann-Hilbert problem for a homogeneous GL(N, C) loop group. Reduction requires the dressing matrices to be fixed points of a loop group automorphism of order two resulting in a sub-hierarchy of gl(N,C) hierarchy containing only odd symmetry flows. The model possesses Virasoro symmetry and imposing Virasoro constraints ensures homogeneity property of the Darboux-Egoroff structure. Dressing matrices of the reduced model provide solutions of the WDVV equations.

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Henrik Aratyn, Johan van de Leur. 2001-11-27. Integrable Structure behind WDVV Equations. https://arxiv.org/abs/hep-th/0111243

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