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

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.

52 pages; v2: some references added, minor textual changes; v3: small corrections to appendix A and (3.35); v4: normalisation of (B.9) corrected, sign of "eps eps R^4" changed to conform with natural conventions

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• Manifestly supersymmetric M-theory
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• Light-cone Quantum Mechanics of the Eleven-dimensional Superparticle
• Vertex Operators for the Supermembrane
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• Generalised 11-dimensional supergravity
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