Self-dual strings and N = 2 supersymmetric field theory (original) (raw)

We show how the Riemann surface of N = 2 Yang-Mills eld theory arises in type II string compactications on Calabi-Yau threefolds. The relevant local geometry is given by brations of ALE spaces. The 3-branes that give rise to BPS multiplets in the string descend to self-dual strings on the Riemann surface, with tension determined by a canonically xed Seiberg-Witten dierential . This gives, eectively, a dual formulation of Yang-Mills theory in which gauge bosons and monopoles are treated on equal footing, and represents the rigid analog of type II-heterotic string duality. The existence of BPS states is essentially reduced to a geodesic problem on the Riemann surface with metric jj 2 . This allows us, in particular, to easily determine the spectrum of stable BPS states in eld theory.

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