The structure of: preliminaries
Remember that
should take values in some representation
of the bosonic group, so in constructing the covariant exressions we should take into account the structure of
We assume 2 things about
The quadratic Casimir of
vanishes (this is the difference of the two Casimirs)
Exists a vector
invariant under
These two conditions are actually quite restrictive. The first condition implies that
. The second condition implies that it is actually contained in the harmonic functions.
Basically, what we are doing is starting from the dilaton/axion waves corresponding to
, and then reconstructing other linearized solutions by acting with the SUSY transformations, as e.g. in (13)
