Consistent off-shell string amplitudes

Based on the covariant loop calculus developed by Di Vecchia et al. and by Petersen et al., we construct consistent, modular-invariant, off-shell closed string amplitudes. Our prescription resolves improper non-localities in the would-be off-shell amplitudes of the covariant loop calculus, thereby eliminating on-shell ambiguities in corners of punctured moduli space and deriving consistent renormalization constants in the infinite-tension limit. We also show that, contrary to expectations, the on-shell limit of the amplitudes in general string models depends on the fixing of the projective freedom inherent in the covariant loop calculus. (orig.)