Supersymmetric higher-derivative actions in ten and eleven dimensions, the associated superalgebras and their formulation in superspace

TL;DR

This paper derives the supersymmetric completion of higher-derivative R^4 terms in eleven-dimensional supergravity, analyzing their effects on supersymmetry algebra and superspace constraints, with implications for string and M-theory effective actions.

Contribution

It provides the explicit supersymmetric completion of R^4 terms in eleven dimensions and links these to superspace formulations, clarifying their impact on superalgebras and torsion constraints.

Findings

Supersymmetric R^4 action completed to second order in fermions.

Modifications to supersymmetry algebra coefficients derived.

No modifications to supertorsion constraints induced by these interactions.

Abstract

Higher-derivative terms in the string and M-theory effective actions are strongly constrained by supersymmetry. Using a mixture of techniques, involving both string amplitude calculations and an analysis of supersymmetry requirements, we determine the supersymmetric completion of the R^4 action in eleven dimensions to second order in the fermions, in a form compact enough for explicit further calculations. Using these results, we obtain the modifications to the field transformation rules and determine the resulting field-dependent modifications to the coefficients in the supersymmetry algebra. We then make the link to the superspace formulation of the theory and discuss the mechanism by which higher-derivative interactions lead to modifications to the supertorsion constraints. For the particular interactions under discussion we find that no such modifications are induced.