Heterotic — type I superstring duality and low-energy effective actions

We compare order R⁴ terms in the 10-dimensional effective actions of SO(32) heterotic and type I superstrings from the point of view of duality between the two theories. Some of these terms do not receive higher-loop corrections being related by supersymmetry to 'anomaly-cancelling' terms which depend on the antisymmetric 2-tensor. At the same time, the consistency of duality relation implies that the 'tree-level' R⁴ super-invariant (the one which has ζ(3)-coefficient in the sphere part of the action) should appear also at higher orders of loop expansion, i.e. should be multiplied by a non-trivial function of the dilaton.