| Motivated by phenomenological applications, in this thesis we study compactifications of Type II, M-theory, and F-theory on Calabi-Yau four-folds. Trying to understand and analytically control compactifications on Calabi-Yau four-folds we obtain a number of interesting results that include new superspace formulations of two-dimensional N = (2,2) and N = (0,4) dilaton supergravity theories coupled to matter; geometric engineering of N = 2 (superconformal) field theories in two and three dimensions; and computation of the effective superpotentials induced by background fluxes and five-brane instantons. |
