Regular R-R and NS-NS BPS black holes

TL;DR

The paper tackles the problem of unifying macroscopic and microscopic descriptions of regular 1/8 BPS black holes in $N=8$ supergravity by exploiting STU truncations and $S\times T$ duality to classify embeddings as NS-NS or RR. It advances the solvable Lie algebra (SLA) framework to provide two distinct ten-dimensional realizations (Type IIB and its Type IIA T-dual) and an algebraic characterization of the RR/NS-NS embeddings, enabling a systematic microscopic interpretation of STU solutions. A concrete four-parameter dilatonic RR solution is analyzed, yielding a macroscopic entropy $S_{macro}=2\pi\sqrt{q_0 p^1 p^2 p^3}$ and a microscopic D0/D4-brane bound-state description with $N_0=q_0$, $N_i=p^i$, giving $S_{micro}=2\pi\sqrt{N_0 N_1 N_2 N_3}$ that matches the macroscopic result. The approach offers a principled dictionary for translating between $N=8$ supergravity embeddings and their string theory microscopic pictures, with potential to illuminate NS-NS configurations and broader U-duality families of black holes.

Abstract

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 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 article 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.