All-loop gauge couplings from anomaly cancellation in string effective theories

We derive, to all orders in perturbation theory, the E8 gauge coupling and the modified dilaton-axion Kähler potential for the effective theories of a class of d = 4, N = 1 heterotic string models. The derivation relies on an extended version of the Green-Schwarz anomaly cancellation mechanism, and exploits target-space duality invariance. Although we deal with field-dependent effective gauge couplings and scales in a non-renormalizable supergravity theory, we derive for them a renormalization group equation as a relation among dynamical fields. When expectation values of these fields are considered, our results agree with those previously obtained in renormalizable theories with N = 1 global supersymmetry. We finally comment on possible generalizations of the present results. © 1991.