Decoupling limit, lens spaces and Taub-NUT: D = 4 black-hole microscopics from D = 5 black holes Original Research Article

We study the space-times of extremal and 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 four-dimensional transverse space of the NUT configuration in D = 5 is foliated by surfaces that are cyclic lens spaces S3/ZN, where N is the quantised monopole charge. By contrast, in D = 4 the three-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.