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

TL;DR

This paper investigates S-duality invariant dilaton couplings at order α'^3 in superstring theory, confirming their form through scattering amplitudes and demonstrating invariance under duality transformations.

Contribution

It derives and confirms S-duality invariant dilaton couplings at order α'^3 using scattering amplitudes and duality symmetry considerations.

Findings

Confirmed the form of dilaton couplings via four-point scattering amplitudes.

Validated the presence of specific terms in the tree-level effective action.

Demonstrated S-duality invariance of the couplings.

Abstract

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. The coupling $\eps_{10}\eps_{10}R^4$ is a total derivative term at four-field level. The $\sigma$-model beta function approach implies the presence of this term at the tree-level. By examining the sphere-level scattering amplitude of five gravitons, we have also confirmed the presence of this term in the tree-level effective action.