$O(9,9)$ symmetry of NS-NS couplings at order $\alpha'^3$

TL;DR

This paper demonstrates that NS-NS couplings at order α'^3 in string theory are invariant under the larger O(9,9) symmetry group when considering cosmological reductions, extending previous O(1,1) symmetry results.

Contribution

The paper extends the known O(1,1) symmetry of NS-NS couplings to the full O(9,9) symmetry at order α'^3 using cosmological reduction techniques.

Findings

NS-NS couplings are invariant under O(9,9) transformations

Field redefinitions and total derivatives do not affect invariance

Supports larger symmetry structures in string effective actions

Abstract

Recently, imposing the $O(1,1)$ symmetry on the circle reduction of the classical effective action of string theory, we have found all NS-NS couplings of type II superstring theories at order $\alpha'^3$. In this paper we use the cosmological reduction on the couplings and show that, up to field redefinitions and total derivative terms, they are invariant under the $O(9,9)$ transformations.