Abstract
We derive the component structure of 11D, N = 1/8 supergravity linearized around eleven-dimensional Minkowski space. This theory represents 4 local supersymmetries closing onto 4 of the 11 spacetime translations without the use of equations of motion. It may be interpreted as adding 201 auxiliary bosons and 56 auxiliary fermions to the physical supergravity multiplet for a total of 376 + 376 components. These components and their transformations are organized into representations of SL(2; C) × G2.
Highlights
Supersymmetries to close on the fields is by terms that vanish if the equations of motion are imposed.1 In this context, the supersymmetry is said to close on-shell only, and the set is referred to as an on-shell supermultiplet
The supersymmetry is said to close on-shell only, and the set is referred to as an on-shell supermultiplet. This should not be interpreted to mean that the component fields in the theory are required to be on-shell; only that the supersymmetries do not close on the off-shell realization
An immediate indication of the inadequacy of any step-wise approach attempting to add suitable component fields and transformations was provided by Siegel and Roček [1]: for any non-real representation in theories with eight or more supersymmetries, any potential solution to this problem requires an infinite number of fields
Summary
The component fields of eleven-dimensional supergravity consist of a frame ema, a gauge 3-form Cmnp, and a gravitino ψmα Under linearized supersymmetry, they transform into each other as δ eab = ̄Γbψa δ Cabc = 3 ̄Γ[abψc]. R, Γai , and j i appearing here are combinations of the more basic auxiliary fields dX , yai , dij, f ijk fields in table 3 and components of the 4-form field strength We present the result of acting with fermionic superspace derivatives in all possible ways on the gravitino components in appendix D. This demonstrates the consistency of the scheme and generates the supersymmetry transformations of the eleven-dimensional gravitino components reported above in (1.6)
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