MIRROR SYMMETRY, N=1 SUPERPOTENTIALS AND TENSIONLESS STRINGS ON CALABI-YAU 4-FOLDS

We study aspects of Calabi-Yau four-folds as compactification manifold s of F-theory, using mirror symmetry of toric hypersurfaces. Correlati on functions of the topological field theory are determined directly i n terms of a natural ring structure of divisors and the period integra ls, and subsequently used to extract invariants of moduli spaces of ra tional curves subject to certain conditions. We then turn to the discu ssion of physical properties of the space-time theories, for a number of examples which are dual to E-8 X 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 comple te 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 appearance of tensi onless strings'. In some cases non-perturbative effects generate an ev erywhere non-zero quantum tension leading to a combination of a conven tional field theory with light strings hiding at a low energy scale re lated to supersymmetry breaking. (C) 1997 Elsevier Science B.V.