5-BRANE EFFECTIVE-FIELD THEORY ON CALABI-YAU 3-FOLDS

We consider the compactification of the dual form of N = 1, D = 10 sup ergravity on a six-dimensional Calabi-Yau manifold. An N = 1 off-shell supergravity effective Lagrangian in four dimensions can be construct ed in a dual version of the gravitational sector (new-minimal supergra vity form). Superspace duality has a simple interpretation in terms of Poincare duality of two-form cohomology. The resulting 4D Lagrangian may describe the low-energy point-field limit of a five-brane theory, dual to string theory, provided Calabi-Yau spaces are consistent vacua of such dual theory.