More Evidence for the WDVV Equations in N=2 SUSY Yang-Mills Theories

Details More Evidence for the WDVV Equations in N=2 SUSY Yang-Mills Theories More Evidence for the WDVV Equations in N=2 SUSY Yang-Mills Theories

1997-01-23

arxiv.org/abs/hep-th/9701123v1

Int.J.Mod.Phys. A15 (2000) 1157-1206

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 40 pages, no figures

Scientific paper

10.1142/S0217751X00000537

We consider 4d and 5d N=2 supersymmetric theories and demonstrate that in general their Seiberg-Witten prepotentials satisfy the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. General proof for the Yang-Mills models (with matter in the first fundamental representation) makes use of the hyperelliptic curves and underlying integrable systems. A wide class of examples is discussed, it contains few understandable exceptions. In particular, in perturbative regime of 5d theories in addition to naive field theory expectations some extra terms appear, like it happens in heterotic string models. We consider also the example of the Yang-Mills theory with matter hypermultiplet in the adjoint representation (related to the elliptic Calogero-Moser system) when the standard WDVV equations do not hold.

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