Decoupling Limit, Lens Spaces and Taub-NUT: D=4 Black Hole Microscopics from D=5 Black Holes

TL;DR

This paper explores the relationship between 4D and 5D black hole microscopics in string theory, focusing on NUT and GPS monopole configurations, and demonstrates how certain p-brane solutions relate through dimensional reduction and U-duality.

Contribution

It provides a new geometric interpretation of D=4 black hole microscopics via D=5 configurations with lens space foliations, linking monopoles and black hole constituents.

Findings

4D transverse space foliated by S^3/Z_N lens spaces

D=4 GPS monopole foliated by 2-spheres

p-brane configurations derived from flat space via dualities

Abstract

We study the space-times of non-extremal intersecting p-brane configurations in M-theory, where one of the components in the intersection is a ``NUT,'' i.e. a configuration of the Taub-NUT type. Such a Taub-NUT configuration corresponds, upon compactification to D=4, to a Gross-Perry-Sorkin (GPS) monopole. We show that in the decoupling limit of the CFT/AdS correspondence, the 4-dimensional transverse space of the NUT configuration in D=5 is foliated by surfaces that are cyclic lens spaces S^3/Z_N, where N is the quantised monopole charge. By contrast, in D=4 the 3-dimensional transverse space of the GPS monopole is foliated by 2-spheres. This observation provides a straightforward interpretation of the microscopics of a D=4 string-theory black hole, with a GPS monopole as one of its constituents, in terms of the corresponding D=5 black hole with no monopole. Using the fact that the near-horizon region of the NUT solution is a lens space, we show that if the effect of the Kaluza-Klein massive modes is neglected, p-brane configurations can be obtained from flat space-time by means of a sequence of dimensional reductions and oxidations, and U-duality transformations.