On the Geometry of Moduli Space of Vacua in N=2 Supersymmetric Yang-Mills Theory

Details On the Geometry of Moduli Space of Vacua in N=2 Supersymmetric Yang-Mills Theory On the Geometry of Moduli Space of Vacua in N=2 Supersymmetric Yang-Mills Theory

1994-08-05

arxiv.org/abs/hep-th/9408036v1

Phys.Lett. B339 (1994) 71-76

Physics

High Energy Physics

High Energy Physics - Theory

10 pgs (TeX with harvmac), POLFIS-TH.07/94, CERN-TH.7384/94

Scientific paper

10.1016/0370-2693(94)91134-7

We consider generic properties of the moduli space of vacua in $N=2$ supersymmetric Yang--Mills theory recently studied by Seiberg and Witten. We find, on general grounds, Picard--Fuchs type of differential equations expressing the existence of a flat holomorphic connection, which for one parameter (i.e. for gauge group $G=SU(2)$), are second order equations. In the case of coupling to gravity (as in string theory), where also ``gravitational'' electric and magnetic monopoles are present, the electric--magnetic S duality, due to quantum corrections, does not seem any longer to be related to $Sl(2,\IZ)$ as for $N=4$ supersymmetric theory.

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