: SUGRA data

The main ingredient is the symmetry group and its Lie superalgebra ,
generated by (in the flat space limit,
will become Poincare translations, left SUSYs and right SUSYs).

The principal bundle is used
(instead of ) as the target space. It is parametrized by the group element :

where . The action is built from currents:

The map is given by the left shifts:

It is straightforward to verify the SUGRA constraints (8):

this is the simplest way to see that is a solution of the Type IIB SUGRA