Four dimensional N=1 supersymmetrization of R^4 in superspace

TL;DR

This paper constructs a four-dimensional N=1 supersymmetric action incorporating an R^4 term, analyzing its on-shell torsions and curvatures, and exploring the implications of the coupling constant on the superspace geometry.

Contribution

It provides the first explicit superspace formulation of R^4 terms in four-dimensional N=1 supergravity, including iterative solutions for torsions and curvatures.

Findings

Derived on-shell torsions and curvatures up to second order in the R^4 coupling

Identified infinite series structure in the solutions for some superspace quantities

Discussed potential extensions to higher dimensions

Abstract

We write an action, in four dimensional N=1 curved superspace, which contains a pure R^4 term with a coupling constant. Starting from the off-shell solution of the Bianchi identities, we compute the on-shell torsions and curvatures with this term. We show that their complete solution includes, for some of them, an infinite series in the R^4 coupling constant, which can only be computed iteratively. We explicitly compute the superspace torsions and curvatures up to second order in this coupling constant. Finally, we comment on the lifting of this result to higher dimensions.