Scaling solutions of N = 2 supergravity and holography

Abstract

The 4D N = 2 SUGRA is the low energy limit of Type II string theory compactified on a Calabi-Yau three-fold. The theory contains BPS black holes with multi centered configurations consisting of bound states of dyonic single-centered black holes. These stationary solutions have an intrinsic angular momentum originating in electro magnetic interaction between charges. A subset of this family called “scaling solutions” for which the relative distances between centers are constrained up to a scale. Contrary to the asymptotically flat non-scaling cases, scaling solutions have an AdS2 factor in their asymptotic geometry and their total angular momentum vanishes. We showed that the AdS2 spacetime at far infinity is equipped with an S2 fiber called a “twist”. It can be thought of as a rotating two-sphere whose angular velocity is determined by the total charge and the total dipole moment of the black hole. In the absence of an angular momentum, the twist can be considered as a topological hair of this family of supersymmetric black holes. It provides a new asymptotic observable to distinguish different black hole solutions. Moreover, to have a better understanding of the twist and its potential role in a quantum theory of supersymmetric black holes, we S2 reduced the asymptotic geometry of the scaling solutions. That leads to an effective 2D theory with an AdS2 geometry and a single U(1) gauge field presenting the twist. Consequently, one would expect the AdS/CFT correspondence to clarify the role of the twist as a new hair of these black holes.