A Puzzle Concerning String Dualities at Order $\alpha'^{\,3}$

We show that the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order $\alpha'^{\,3}$, with overall coefficient proportional to $\zeta(3)$, is not invariant under standard $O(9,9)$ transformations. This is in conflict with the general result in string theory, due to Sen, that classical string theory with $d$-dimensional translation invariance admits an $O(d,d)$ symmetry to all orders in $\alpha'$. Possible resolutions of this puzzle are discussed.