## Evidence for F-theory.(English)Zbl 1003.81531

Summary: We construct compact examples of $$D$$-manifolds for type IIB strings. The construction has a natural interpretation in terms of compactification of a 12-dimensional F-theory. We provide evidence for a more natural reformulation of type IIB theory in terms of F-theory. Compactification of M-theory on a manifold $$K$$ which admits elliptic fibration is equivalent to compactification of $$F$$-theory on $$K\times S^{1}$$. A large class of $$N=1$$ theories in 6 dimensions are obtained by compactification of F-theory on Calabi-Yau threefolds. A class of phenomenologically promising compactifications of $$F$$-theory is on Spin(7) holonomy manifolds down to 4 dimensions. This may provide a concrete realization of Witten’s proposal for solving the cosmological constant problem in four dimensions.

### MSC:

 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 32J17 Compact complex $$3$$-folds 32J81 Applications of compact analytic spaces to the sciences 83E30 String and superstring theories in gravitational theory
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