Abstract
We present an action for N = 1 supergravity in 10 + 2 dimensions, containing the gauge fields of the OSp(1|64) superalgebra, i.e. one-forms B (n) with n=1,2,5,6,9,10 antisymmetric D=12 Lorentz indices and a Majorana gravitino ψ. The vielbein and spin connection correspond to B (1) and B (2) respectively. The action is not gauge invariant under the full OSp(1|64) superalgebra, but only under a subalgebra \( \tilde{F} \) (containing the F algebra OSp(1|32)), whose gauge fields are B (2), B (6), B (10) and the Weyl projected Majorana gravitino \( \frac{1}{2}\left(1+{\Gamma}_{13}\right)\psi \). Supersymmetry transformations are therefore generated by a Majorana-Weyl supercharge and, being part of a gauge superalgebra, close off-shell. The action is simply ∫STr(R 6 Γ) where R is the OSp(1|64) curvature supermatrix two-form, and Γ is a constant supermatrix involving Γ13 and breaking OSp(1|64) to its \( \tilde{F} \) subalgebra. The usual Einstein-Hilbert term is included in the action.
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Castellani, L. A locally supersymmetric SO(10, 2) invariant action for D = 12 supergravity. J. High Energ. Phys. 2017, 61 (2017). https://doi.org/10.1007/JHEP06(2017)061
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DOI: https://doi.org/10.1007/JHEP06(2017)061