A locally supersymmetric SO(10, 2) invariant action for D = 12 supergravity

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 F ̃ (containing the F algebra OSp(1|32)), whose gauge fields are B(2), B(6), B(10) and the Weyl projected Majorana gravitino 1 (1 + Γ13)ψ. Supersymmetry transformations are therefore generated 2 by a Majorana-Weyl supercharge and, being part of a gauge superalgebra, close off-shell. The action is simply STr(R6Γ) 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 F ̃ subalgebra. The usual Einstein-Hilbert term is included in the action.