Effective Field Equations for Fermionic Strings

We show how to obtain loop-corrected effective field equations in tachyon-free heterotic string theories. The corrections are automatically gauge-invariant; they simultaneously secure Brst-decoupling and unambiguous loop amplitudes. We introduce a cutoff for two-dimensional field theory which is more general than the choice of a world-sheet metric, and using this we give an invariant description of factorization of fermionic amplitudes. As an example we work out the linearized corrections for the O(16) × O(16) heterotic string. They come from a finite corrected effective action.