Integrable Structure Behind the WDVV Equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 18-31
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An integrable structure behind the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations is identified with the reduction of the Riemann–Hilbert problem for the homogeneous loop group $\widehat{GL}(N,\mathbb C)$. The reduction requires the dressing matrices to be fixed points of an order-two loop group automorphism resulting in a subhierarchy of the $\widehat{gl}(N,\mathbb C)$ hierarchy containing only odd-symmetry flows. The model has Virasoro symmetry; imposing Virasoro constraints ensures the homogeneity property of the Darboux–Egoroff structure. Dressing matrices of the reduced model provide solutions of the WDVV equations.
Keywords:
WDVV equations, dressing, Darboux–Egoroff metrics, Kadomtsev–Petviashvili hierarchies, tau functions, Riemann–Hilbert factorization.
@article{TMF_2003_134_1_a2,
author = {Kh. Aratin and Zh. van de Ler},
title = {Integrable {Structure} {Behind} the {WDVV} {Equations}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {18--31},
publisher = {mathdoc},
volume = {134},
number = {1},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a2/}
}
Kh. Aratin; Zh. van de Ler. Integrable Structure Behind the WDVV Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 18-31. http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a2/