On SO(32) heterotic - type I superstring duality in ten dimensions

We provide some additional evidence in favour of the strong - weak coupling duality between the SO(32) heterotic and type I superstring theories by comparing terms quartic in the gauge field strength in their low-energy effective actions. We argue that these terms should not receive higher-loop string corrections so that duality should relate the leading-order perturbative coefficients in the two theories. In particular, we demonstrate that the coefficient of the $F^4$-term in the one-loop (torus) part of the SO(32) heterotic string action is exactly the same as the coefficient of the $F^4$-term in the tree-level (disc) part of the type I action.Comment: 11 pages, harvmac. Several comments added, final version to appear in Physics Letters

Natural Suppression of Higgsino-Mediated Proton Decay in Supersymmetric SO(10)

In supersymmetric Grand Unified Theories, proton decay mediated by the color--triplet higgsino is generally problematic and requires some fine--tuning of parameters. We present a mechanism which naturally suppresses such dimension 5 operators in the context of SUSY $SO(10)$. The mechanism, which implements natural doublet--triplet splitting using the adjoint higgs, converts these dimension 5 operators effectively into dimension 6. By explicitly computing the higgs spectrum and the resulting threshold uncertainties we show that the successful prediction of $\sin^2\theta_W$ is maintained {\it as a prediction} in this scheme. It is argued that only a weak suppression of the higgsino mediated proton decay is achievable within SUSY $SU(5)$ without fine--tuning, in contrast to a strong suppression in SUSY $SO(10)$.Comment: 39 pages (3 Feynman graphs not included), in Plain LaTeX, BA-93-2