HETEROTIC - TYPE-I SUPERSTRING DUALITY AND LOW-ENERGY EFFECTIVE ACTIONS

We compare order R(4) terms in the 10-dimensional effective actions of SO(32) heterotic and type I superstrings from the point of view of du ality between the two theories. Some of these terms do not receive hig her-loop corrections being related by supersymmetry to 'anomaly-cancel ling' terms which depend on the antisymmetric 2-tensor. At the same ti me, the consistency of duality relation implies that the 'tree-level' R(4) super-invariant (the one which has zeta(3)-coefficient in the sph ere part of the action) should appear also at higher orders of loop ex pansion, i.e. should be multiplied by a non-trivial function of the di laton.