Integrable Structure behind WDVV Equations
High Energy Physics - Theory
2007-05-23 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.hep-th/0111243,
title = {Integrable Structure behind WDVV Equations},
author = {Henrik Aratyn and Johan van de Leur},
journal= {arXiv preprint arXiv:hep-th/0111243},
year = {2007}
}
Comments
14 pgs, contribution to Needs 2001 conference proceedings