Ten- and eleven-dimensional perspectives on N = 2 black holes

Abstract

We give an 11- and 10-dimensional supergravity description of M5-branes wrapping 4-cylces in a Calabi–Yau manifold and carrying momentum along a transverse S1. These wrapped branes descend to a class of N = 2 black holes in 4 dimensions. Our description gives the conditions on the geometry interpolating between the asymptotic and near-horizon regions. We employ the ideas of geometric transitions to show that the near-horizon geometry in 10 dimensions is AdS2 × S2 × CY3 while in 11 dimensions it is AdS3 × S2 × CY3. We also show how to obtain the complete N = 2 black hole supergravity solution in 4 dimensions for this class of black holes starting with our 11-dimensional description. Finally, we generalize our results on the 10- and 11-dimensional near-horizon supergravity solution to the case of black holes carrying arbitrary charges (D0–D2–D4–D6 in type IIA description). We argue that the near-horizon geometry corresponding to wrapped D6 and D2 branes in 11 dimensions is AdS2 × S3 × CY3.