HOLOGRAPHIC BLACK OBJECTS

One of the most interesting applications of the AdS/CFT correspondence relies on the fact that, from a holographic point of view, the microstates of a black hole correspond to a set of states in the dual field theory with the same charges of the black hole, whose entropy can thus be reproduced from a state counting in the dual field theory. For instance, the entropy of asymptotically AdS5 supersymmetric rotating black holes can be obtained extremizing an entropy function that arises opportunely managing the four-dimensional superconformal index. The first part of this thesis is devoted to the analysis of the saddle-point expansion in the so-called Cardy-like limit of the index for different SCFTs. Besides presenting new insights on the structure of such expansion, these results could provide some hints on its dual gravitational interpretation. The holographic counterpart of the extremization of the entropy function is given by the attractor mechanism, which for rotating five-dimensional black holes is still unknown. However, as we discuss in the second part of this work, this lack can be circumvented by performing a compactification on the five-dimensional black hole and then using the attractor mechanism on the resulting four-dimensional one. Finally, other interesting instances come from the compactification of SCFTs on curved spaces, which allows to define new field theories in lower dimensions. The extremization procedure carried out in field theory to derive the central charge of the (even) lower-dimensional theory corresponds holographically to an extremization problem in supergravity that resemble the attractor mechanism. When the original theory is compactified on a two-dimensional orbifold known as spindle, this mechanism exhibits new peculiar features, as we present in the last part of this thesis. For example, the spinors are not constant on such orbifolds.