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

TL;DR

This paper verifies that the order  corrections in string theory's effective action are consistent with an (9,9) symmetry after cosmological reduction, confirming a conjecture about string dualities at higher orders.

Contribution

It demonstrates that the  order  corrections preserve the (9,9) symmetry in cosmological reduction, supporting the conjecture of (d,d) symmetry at all orders in .

Findings

The  corrected terms are compatible with (9,9) symmetry.

The results confirm the conjecture of (d,d) symmetry at all orders in .

The cosmological reduction preserves the duality symmetry at order .

Abstract

We compute 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 $\zeta(3)$, 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 $\alpha'$.