Seminario di fisica teorica
Since the proposal of the AdS/CFT correspondence, several examples of this conjecture involving branes wrapped on smooth Riemann surfaces $Sigma$ have appeared in the literature. In all these constructions, the $D=10,11$ supergravity solutions exhibit a boundary of the schematic form $AdS_{d+1}times M_{D-(d+1)}$ and a near-horizon geometry of the type $AdS_{d+1-n}times Sigma_ntimes M_{D-(d+1)}$, where $M$ is a compact manifold. After reducing the higher-dimensional theory on $M$, these solutions are interpreted as black branes in $AdS_{d+1}$ wrapped on $Sigma$. In this setup, supersymmetry is preserved via the so-called topological twist, which ensures that the supersymmetry spinor is independent of the coordinates on $Sigma$. A pivotal shift occurred with the work arXiv:2011.10579, which showed that branes could also be wrapped on orbifolds (specifically, the spindle). This breakthrough revealed that supersymmetry can be preserved in a completely novel way through the anti-twist, an orbifold generalization of the no-twist. Following this, significant efforts have been devoted to constructing similar and even more intricate solutions. Of particular interest is the case $d=1$, as the resulting metric is expected to correspond to the near-horizon limit of supersymmetric black holes in string theory. In the first part of this seminar, I will introduce the main characters of this game, with a focus on why black holes play a central role in the study of quantum gravity. I will then discuss my current research on spindles, with reference to arXiv:2210.16128, arXiv:2402.08724 and arXiv:2409.xxxxx.