Closed bosonic strings in background gauge fields

The coupling to abelian background gauge fields of closed bosonic strings compactified on a torus is considered. There exist specific field configurations for which the theory cannot be defined consistently, in spite of the fact that the field equations of motion are then solved exactly. This critical behaviour is related to a breakdown of local and global world-sheet symmetries, as well as of spacetime unitarity. A physical interpretation of this phenomenon is proposed. The issue of spacetime duality is also discussed. This symmetry is shown to be partially broken for generic background field configurations.