The $\hat{G}^{4}λ^{16}$ Term in IIB Supergravity

TL;DR

This work determines the τ-dependence of the $\hat{G}^{4}\lambda^{16}$ coupling in the type IIB effective action by enforcing supersymmetry and $SL(2,\mathbb{Z})$ duality. Using a Noether-based SUSY analysis, the coefficient is shown to be the modular form $D^{14}E_{5/2}$, i.e., the Eisenstein-series structure acted on by 14 covariant derivatives, consistent with tree-level, loop, and D-instanton contributions. The result extends the established α'^3 λ^{16} sector, which obeys a Laplacian eigenvalue equation and aligns with prior conjectures about higher-derivative terms in the IIB action. Overall, the paper strengthens the link between supersymmetry, duality, and non-perturbative effects in the IIB effective action and informs the structure of higher-derivative interactions.

Abstract

The supersymmetry constraints on the $\hat{G}^{4}\lamda^{16}$ term in the effective action of type IIB superstring theory are studied in order to determine the dependence of its coefficient on the complex scalar field, $τ$. The resulting expression is consistent with the $SL(2,{\Bbb Z})$ invariant conjectures in the literature.