ε∇4R4 type invariants and their gradient expansion

We analyse the constraints from supersymmetry on ∇4R4 type corrections to the effective action in N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=2 $$\end{document} supergravity in eight dimensions. We prove that there are two classes of invariants that descend respectively from type IIA and type IIB supergravity. We determine the first class as d-closed superforms in superspace in eight dimensions, whereas we obtain the second class by dimensional reduction down to four dimensions, in which there is a single class of invariants transforming in the next to minimal unitary representation of E7(7).