Regular BPS black holes: macroscopic and microscopic description of the generating solution

In this paper we construct the BPS black hole generating solution of toroidally compactified string (and M) theory, giving for it both the macroscopic and microscopic description. Choosing a proper U-duality gauge the latter will be given by a bound state made solely of D-branes. The axionic nature of the supergravity solution will be directly related to non-trivial angles between the constituent D-branes (type IIB configuration) or, in a T-dual gauge, to the presence of magnetic flux on constituent D-brane world volumes (type IIA configuration). As expected, the four dimensional axion fields arise from the dimensional reduction of non-diagonal metric tensor components or Kalb-Ramond B field components for type IIB or type IIA cases, respectively. Thanks to this result it is then now possible to fill the full 56-dimensional U-duality orbit of N=8 BPS black holes and to have a macroscopic and microscopic description of all of them.