SUGRA-Data

SUGRA data

Now we define

and

— collections of vector fields on

by this formula:

(there is an imbiguity called “shift transformations” — see next slide).

We can now continue describing the SUGRA data. We got:

(7)

satisfying the following properties:

commutes with the action of
is “fixed modulo ” in the following sense: for any point let be the natural projection , then
(in other words, only the vertical component of is non-obvious; the projection to is tautological)
SUGRA constraints:
(8)
where:
- and are some sections of and
- , and some sections of (i.e. vertical vector fields); they are essentially “curvatures”

Notice that satisfying the SUGRA constraints does depend on the vertical component of