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Exact results for $$N=2$$ compactifications of heterotic strings. (English) Zbl 0957.14509
Summary: We search for $$N=2$$, $$d=4$$ theories which can be realized both as heterotic string compactifications on $$K3\times T^2$$ and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative superpotential of one string theory is given in terms of tree level computations in the other string theory. In particular we find concrete examples which provide the stringy realization of the results of Seiberg and Witten on $$N=2$$ Yang-Mills theory, corrected by gravitational/stringy effects. We also discuss some examples which shed light on how the moduli spaces of different $$N=2$$ heterotic vacua are connected.

MSC:
 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 32G81 Applications of deformations of analytic structures to the sciences
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