Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-10-21
Nucl.Phys. B494 (1997) 489-545
Physics
High Energy Physics
High Energy Physics - Theory
68 pages, harvmac.tex, references added, minor corrections, Comments on phase transitions in sect. 5. added, two figures added
Scientific paper
10.1016/S0550-3213(97)00196-X
We study aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces. Correlation functions of the topological field theory are determined directly in terms of a natural ring structure of divisors and the period integrals, and subsequently used to extract invariants of moduli spaces of rational curves subject to certain conditions. We then turn to the discussion of physical properties of the space-time theories, for a number of examples which are dual to $E_8\times E_8$ heterotic N=1 theories. Non-critical strings of various kinds, with low tension for special values of the moduli, lead to interesting physical effects. We give a complete classification of those divisors in toric manifolds that contribute to the non-perturbative four-dimensional superpotential; the physical singularities associated to it are related to the apppearance of tensionless strings. In some cases non-perturbative effects generate an everywhere non-zero quantum tension leading to a combination of a conventional field theory with light strings hiding at a low energy scale related to supersymmetry breaking.
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