: 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):