$\mathcal{E}{\nabla }^4{R}^4$ type invariants and their gradient expansion

Abstract

We analyse the constraints from supersymmetry on ${\nabla }^4{R}^4$ type corrections to the effective action in $\mathcal{N}=2$ 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 $E_{7(7)}$.

arXiv comment53 pages, minor corrections, published version in JHEP

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