FIVEBRANES, MEMBRANES AND NONPERTURBATIVE STRING THEORY

Non-perturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a Calabi-Yau space are derived and found to contain order e(-1/gs) contributions, where g(s) is the string coupling. The computation reduces to a weighted sum of supersym metric extremal maps of strings, membranes and fivebranes into the Cal abi-Yau space, all three of which enter on equal footing. It is shown that a supersymmetric 3-cycle is one for which the pullback of the Kah ler form vanishes and the pullback of the holomorphic three-form is a constant multiple of the volume element, Quantum minor symmetry relate s the sum in the IIA theory over supersymmetric, odd-dimensional cycle s in the Calabi-Yau space to a sum in the IIB theory over supersymmetr ic, even-dimensional cycles in the mirror.