Some global aspects of string compactifications

Nearly flat bosonic string vacua are examined. An analogy between compactification in string theory with tachyonic condensation and the Landau theory of solidification is pointed out. A generic frustration resulting from the incompatibility of the topologies of the plane and that of the sphere is discussed. This is a global obstacle to obtain perturbatively fixed points on compact space-time. Some relations between global properties of the space-time manifolds and the various world-sheet couplings are obtained. These properties serve also as guides to study and solve perturbatively c ≥ d conformal backgrounds.