There and back again: a holographic journey towards black-hole microstates

The microscopic interpretation of the Bekenstein-Hawking entropy is still an open challenge in theoretical physics. Supersymmetric indices and holography, turn out to be major tools to improve our knowledge. In the first part of this thesis, using a Bethe Ansatz formulation, we compute the large $N$ limit of the superconformal index with arbitrary chemical potentials for all charges and angular momenta, for generic 4d $\mathcal{N}=1$ conformal theories with a holographic dual. We conjecture and bring evidence that a particular universal Bethe vacuum dominates the index at large $N$. For $\mathcal{N}=4$ super-Yang-Mills, this contribution correctly leads to the entropy of BPS Kerr-Newman black holes in AdS$_5 \times S^5$ for arbitrary values of the conserved charges, completing the derivation of their microstates. We also consider theories dual to AdS$_5 \times \mathrm{SE}_5$, where SE$_5$ is a Sasaki-Einstein manifold. We first check our results against the so-called universal black hole. We then explicitly construct the near-horizon geometry of BPS Kerr-Newman black holes in AdS$_5 \times T^{1,1}$, charged under the baryonic symmetry of the conifold theory, and with equal angular momenta. We compute their entropy using the attractor mechanism and find complete agreement with the field theory predictions. For BPS black holes with an AdS$_2$ factor at the horizon, the black-hole microstates can be seen as ground states of a dual 1d theory. In the second part of this dissertation, we construct an $\cN=2$ supersymmetric gauged 1d model by starting from the 3d $\cN=2$ Chern-Simons matter theory holographically dual to massive type IIA string theory on AdS$_4 \times S^6$, and Kaluza-Klein reducing it on $S^2$ with a background dual to the asymptotics of static dyonic BPS black holes in AdS$_4$. The background involves a choice of gauge fluxes, that we fix via a saddle-point analysis of the 3d topologically twisted index at large $N$. The ground-state degeneracy of the effective quantum mechanics reproduces the entropy of BPS black holes, and we expect its low-lying spectrum to contain information about near-extremal horizons. Interestingly, the model has a large number of statistically-distributed couplings, reminiscent of SYK-like models.