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

A. Ceresole·R. D'Auria·S. Ferrara
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Abstract

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 $Sl(2,\mathbb{Z})$ as for $N=4$ supersymmetric theory.

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A. Ceresole, R. D'Auria, S. Ferrara. 1994-08-05. On the Geometry of Moduli Space of Vacua in N=2 Supersymmetric Yang-Mills Theory. https://doi.org/10.1016/0370-2693(94)91134-7

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