Type IIB at eight derivatives: insights from Superstrings, Superfields and Superparticles

TL;DR

This paper investigates the structure of eight-derivative couplings in Type IIB superstring theory, using superstring amplitudes, superparticle models, and compactifications to verify duality invariance and derive effective actions.

Contribution

It provides a complete effective action for the maximally R-symmetry-violating sector and confirms SL(2,Z) duality invariance using superparticle amplitudes and superspace methods.

Findings

Matched five-point string amplitudes with superspace integrals and superparticle amplitudes.

Derived the effective action in the R-symmetry-violating sector.

Verified consistency of K3 reductions with six-dimensional supersymmetry.

Abstract

We study the non-linear structure of Type IIB eight-derivative couplings involving the metric and the complexified three-form $G_3$. We show that, at the level of five-point string amplitudes, the kinematics in the maximally R-symmetry-violating sector is fully matched by standard superspace integrals and by superparticle amplitudes in M-theory on a two-torus. The latter approach is used to determine the complete effective action in this sector and to verify its invariance under SL$(2,\mathbb{Z})$ duality. We further comment on the general structure of the higher-point kinematics. Compactifications to lower dimensions provide both tests for our results and the arena for their applications. We verify that K3 reductions are fully consistent with the constraints of six-dimensional supersymmetry, and derive the four-dimensional flux scalar potential and axion kinetic terms at order $(\alpha^{\prime})^{3}$ in Calabi-Yau threefold reductions.