String Dualities at Order ³

We compute the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order alpha'(3), with an overall coefficient proportional to zeta(3), and show that it is compatible with an O(9, 9) symmetry. This confirms the general result in string theory, due to Sen [O(d) x O(d) symmetry of the space of cosmological solutions in string theory, scale factor duality and two-dimensional black holes, Phys. Lett. B 271, 295 (1991)], that classical string theory with d-dimensional translation invariance admits an O(d, d) symmetry to all orders in alpha'.