A note on the RG flow in (N=1, D=4) supergravity and applications to Z(3) orbifold/orientifold compactification

We apply the standard approach of RG flow for the gauge couplings in N = 1, D = 4 supergravity to show how to match its results with the heterotic Z(3 ) orbifold and type IIB Z3 orientifold-based models. Using only supergravit y, anomaly cancellation and the requirement of unification we determine the part of the Kahler potential of the model invariant under the symmetries o f the model. Fur heterotic orbifolds/type IIB orientifolds, this shows that the lowest order Kahler term of the dilaton has the structure - In(S + (S) over bar) in agreement with string calculations. The structure of the holo morphic couplings is also found from arguments of unification and anomaly c ancellation under the conjectured SL(2, Z)(T1) symmetries of the models. A consequence of the latter is that in the case of the Z(3) orientifold the h olomorphic coupling necessarily contains a part with coefficient proportion al to the one loop beta function, in agreement with string calculations whi ch do not however assume this symmetry, This gives circumstantial evidence for the existence of this symmetry at string level in Z(3) orientifold. Fin ally, we comment on the values of the unification scale and examine the pos sibility of mirage unification in which the effective unification scale may be situated far above the string scale. (C) 2001 Elsevier Science B.V. All rights reserved.