Regular R-R and NS-NS BPS black holes

We show in a precise group theoretical fashion how the generating solution of regular BPS black holes of N=8 supergravity, which is known to be a solution also of a simpler N=2 STU model truncation, can be characterized as purely NS–NS or R–R charged according to the way the corresponding STU model is embedded in the original N=8 theory. Of particular interest is the class of embeddings which yield regular BPS black hole solutions carrying only R–R charge and whose microscopic description can possibly be given in terms of bound states of D-branes only. The microscopic interpretation of the bosonic fields in this class of STU models relies on the solvable Lie algebra (SLA) method. In the present paper, we improve this mathematical technique in order to provide two distinct descriptions for type IIA and type IIB theories and an algebraic characterization of S×T-dual embeddings within the N=8, d=4 theory. This analysis will be applied to the particular example of a four parameter (dilatonic) solution of which both the full macroscopic and microscopic descriptions will be worked out.