A.2 supergravity conventions
There is a similar discussion for supergravity  whose gravity supermultiplet
involves metric , a three gauge field potential , or its Hodge dual , and a gravitino
. When embedding this structure in superspace [153, 117], one uses local
coordinates where now stands for an 11-dimensional Majorana spinor having 32 real
components. As before, the superfield encoding information about both the metric and gravitino is the
supervielbein , the superfield extension of the bosonic vielbein . The notation is as
before, with the understanding that the current bosonic indices, both curved and tangent space
, run from 0 to 10. Furthermore, is extended into a superfield 3-form with
superspace components .
As in type IIA and B, it is natural to introduce the field strengths of these superfield potentials
are gauge invariant under the abelian gauge potential transformations
These superfields satisfy the set of constraints
These allow one to establish an equivalence between this superspace formulation and the on-shell
supergravity component one. They are also crucial to proving the kappa symmetry invariance of both M2
and M5-brane actions.