Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-04-08
Nucl.Phys. B477 (1996) 746-766
Physics
High Energy Physics
High Energy Physics - Theory
harvmac, 22p, uses epsf, with 3 .eps figures (references added plus other minor corrections)
Scientific paper
10.1016/0550-3213(96)00353-7
We show how the Riemann surface $\Sigma$ of $N=2$ Yang-Mills field theory arises in type II string compactifications on Calabi-Yau threefolds. The relevant local geometry is given by fibrations 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 fixed Seiberg-Witten differential $\lambda$. This gives, effectively, 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 $|\lambda|^2$. This allows us, in particular, to easily determine the spectrum of {\it stable} BPS states in field theory. Moreover, we identify the six-dimensional space $\IR^4\times \Sigma$ as the world-volume of a five-brane and show that BPS states correspond to two-branes ending on this five-brane.
Klemm Albrecht
Lerche Wolfgang
Mayr Peter
Vafa Cumrun
Warner Nicholas
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