WDVV Equations from Algebra of Forms

Details WDVV Equations from Algebra of Forms WDVV Equations from Algebra of Forms

1997-01-06

arxiv.org/abs/hep-th/9701014v1

Mod.Phys.Lett. A12 (1997) 773-788

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 14 pages, no figures

Scientific paper

A class of solutions to the WDVV equations is provided by period matrices of hyperelliptic Riemann surfaces, with or without punctures. The equations themselves reflect associativity of explicitly described multiplicative algebra of (possibly meromorphic) 1-differentials, which holds at least in the hyperelliptic case. This construction is direct generalization of the old one, involving the ring of polynomials factorized over an ideal, and is inspired by the study of the Seiberg-Witten theory. It has potential to be further extended to reveal algebraic structures underlying the theory of quantum cohomologies and the prepotentials in string models with N=2 supersymmetry.

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