String Dualities at Order ${\alpha }^{\prime 3}$

Abstract

We compute the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order ${\alpha }^{\prime 3}$, with 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, that classical string theory with $d$-dimensional translation invariance admits an $O(d,d)$ symmetry to all orders in ${\alpha }^{\prime }$.

10 pages, v2: Major changes. Puzzle alluded to in the original title has been resolved by finding a computational mistake. Corrected result: the ${\alpha }^{\prime 3}$ corrections with coefficient $\zeta (3)$ are compatible with continuous $O(9,9)$ symmetry. Details of computation and references added, v3: version published in PRL