F-THEORY AND LINEAR SIGMA-MODELS

We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investiga te the four-dimensional duality between (0,2) heterotic and F-theory c ompactifications. We indirectly find that much interesting heterotic i nformation must be contained in the 'spectral bundle' and in its dual description as a gauge theory on multiple F-theory 7-branes. A by-prod uct of these efforts is a method for analyzing semistability and the s plitting type of vector bundles over an elliptic curve given as the sh eaf cohomology of a monad. (C) 1998 Elsevier Science B.V.