LOW-ENERGY ANALYSIS OF M-THEORY AND F-THEORY ON CALABI-YAU THREEFOLDS

We elucidate the interplay between gauge and supersymmetry anomalies i n six-dimensional N = 1 supergravity with generalized couplings betwee n tensor and vector multiplets, We derive the structure of the five-di mensional supergravity resulting from the Si reduction of these models and give the constraints on Chem-Simons couplings that follow from du ality to M-theory compactified on a Calabi-Yau threefold. The duality is supported only on a restricted class of Calabi-Yau threefolds and r equires a special type of intersection form. We derive five-dimensiona l central-charge formulas and briefly discuss the associated phase tra nsitions. Finally, we exhibit connections with F-theory compactificati ons on Calabi-Yau manifolds that admit elliptic fibrations. This analy sis suggests that F-theory unifies type-IIb three-branes and M-theory five-branes.