Ten and eleven dimensional perspectives on N=2 black holes

TL;DR

This paper provides a detailed supergravity description of N=2 black holes arising from wrapped M5-branes in 10 and 11 dimensions, elucidating their near-horizon geometries and charge configurations.

Contribution

It introduces a comprehensive 11D and 10D supergravity framework for N=2 black holes, including geometric transition insights and generalizations to arbitrary charges.

Findings

Near horizon geometry in 10D is AdS2×S2×CY3.

Near horizon geometry in 11D is AdS3×S2×CY3.

Complete 4D supergravity solutions for these black holes are derived.

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 S$^1$. 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 ten dimensions is AdS$_2\times$S$^2\times CY_3$ while in 11 dimensions it is AdS$_3\times$S$^2\times CY_3$. 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 the type IIA description). We argue that the near horizon geometry corresponding to wrapped D6 and D2 branes in 11 dimensions is AdS$_2\times$S$^3\times CY_3$.