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Dual string pairs with $$N=1$$ and $$N=2$$ supersymmetry in four dimensions. (English) Zbl 0957.81590
Summary: Based on a simple adiabatic argument and by considering the heterotic string counterpart of certain symmetries of Type II superstrings such as $$(-1)^FL$$ and orientation reversal, we construct orbifold candidates for dual pairs of heterotic and Type II string theories with $$N=2$$ and $$N=1$$ supersymmetry. We also analyze from a similar point of view the K3 fibrations that enter in recently proposed $$N=2$$ candidates and use this structure together with certain orientation-reversing symmetries to construct $$N=1$$ dual pairs. These pairs involve generalizations of Type I vacua which can be equivalent to $$E_8\times E_8$$ heterotic strings, while standard Type I vacua are related to SO(32).

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 14J28 $$K3$$ surfaces and Enriques surfaces 32G81 Applications of deformations of analytic structures to the sciences
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