Curved 11D Supergeometry

Abstract

We examine the theta-expansion of the eleven-dimensional supervielbein. We outline a systematic procedure which can be iterated to any order. We give explicit expressions for the vielbein and three-form potential components up to order $\mathcal{O}({þ}^5)$. Furthermore we show that at each order in the number of supergravity fields, in a perturbative expansion around flat space, it is possible to obtain exact expressions to all orders in theta. We give the explicit expression at linear order in the number of fields and we show how the procedure can be iterated to any desired order. As a byproduct we obtain the complete linear coupling of the supermembrane to the background supergravity fields, covariantly in component form. We discuss the implications of our results for M(atrix) theory.

32 pages. v2: references and acknowledgment added. v3: includes a new section (4.4) on maximally-supersymmetric spaces; to appear in JHEP

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• Compactification of the Heterotic Pure Spinor Superstring I
• Aspects of D-brane Dynamics in Supergravity Backgrounds with Fluxes, Kappa-symmetry and Equations of Motion. Part IIB
• Eleven dimensional supergravity in light cone gauge
• Chiral supergravity actions and superforms
• Dirac equation for the supermembrane in a background with fluxes from a component description of the D=11 supergravity-supermembrane interacting system
• Flux Vacua and Supermanifolds
• $\beta$-deformation for matrix model of M-theory
• Notes on the $D=11$ pure spinor superparticle
• Flux Quantization on 11-dimensional Superspace
• Peculiarities of String Theory on AdS(4) x CP(3)
• A Landscape of Field Theories
• Constrained Supermanifolds for AdS M-Theory Backgrounds
• All symmetric space solutions of eleven-dimensional supergravity
• The action principle and the supersymmetrisation of Chern-Simons terms in eleven-dimensional supergravity
• De Sitter space from dilatino condensates in (massive) IIA
• Super coset space geometry
• Holographic M-Brane Super-Embeddings
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
• Branes, fermions, and superspace dualities