Conformal invariance of σ-models and classical string physics

We show that the identification of the conformal anomaly of the general bosonic two-dimensional non-linear σ-model as the generating functional for on-shell string scattering amplitudes is correct up to O(α') terms. The absence, in the loop corrections to the spacetime effective action, on contributions from the explicit coupling to the dilaton field is suggested as a general feature for σ-models describing tree-level string physics. (orig.)