Geometric constructions of nongeometric string theories

Abstract

We advocate a framework for constructing perturbative closed string compactifications which cannot be scaled up uniformly to have large-radius limits. The idea is to augment the class of vacua which can be described as flbrations by enlarging the mon-odromy group around the singular fibers to include perturbative stringy duality symmetries. As a controlled laboratory for testing this program, we study in detail six-dimensional (1,0) supersymmetric vacua arising from two-torus flbrations over a two-dimensional base. We also construct some examples of two-torus fibrations over four-dimensional bases, and comment on the extension to other fibrations. © SISSA/ISAS 2004.