Abstract:We derive a precise dictionary between micro-state geometries and open string condensates for a large class of excitations of four dimensional BPS black holes realised in terms of D3-branes intersecting on a six-torus. The complete multipole expansion of the supergravity solutions at weak coupling is extracted from string amplitudes involving one massless closed string and multiple open strings insertions on disks with mixed boundary conditions.

Abstract:We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in R 3 . Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.

We derive the leading g_s perturbation of the SUGRA fields generated by a supersymmetric configuration of respectively 1, 2 or 4 D3-branes intersecting at an arbitrary angle via the computation of the string theory disk scattering amplitude of one massless NSNS field interacting with open strings stretched between the branes. The configuration with four branes is expected to be relevant for black hole microstate counting in four dimensions.Comment: 28 pages, 1 figur