S-duality invariant dilaton couplings at order $\alpha'^3$

Understand

The Riemann curvature correction to the type II supergravity at eight-derivative level is given schematically as $(t_8t_8+{1}{8}\eps_{10}\eps_{10})R^4$ at tree-level.

• The replacement of the generalized Riemann curvature in $t_8t_8R^4$, proposed by Gross and Sloan, produces various NS-NS couplings which are invariant under T-duality.
• Recently, using the combination of S-duality and T-duality transformations on these couplings, we have found groups of couplings which are invariant under the S-duality transformation.
• In this paper, we have examined the couplings involving the dilaton with direct scattering amplitude calculations of four NS-NS vertex operators in the superstring theory and found exact agreement.