Time Variation of Newton's Gravitational Constant in Superstring Theories

Abstract

The present time variation of coupling constants in superstring theories with currently favorable internal backgrounds critically depends on the shape of the potential for the size of the internal space. If the potential is almost flat, as in perturbation theory to all orders, the value of $\frac{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{G}}{G}$ for Newton's gravitational constant is calculable and estimated to be - 1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11\ifmmode\pm\else\textpm\fi{}1}$ ${\mathrm{yr}}^{\ensuremath{-}1}$. If the potential has a minimum with finite curvature due to unknown nonperturbative effects, $\frac{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{G}}{G}$ will become unobservably small. Improvement of the measurement of $\frac{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{G}}{G}$ would discriminate between the two situations. Problems with the time variation of other coupling constants are also discussed.