Finn Larsen

A bstract: We construct the phase diagram of supersymmetric ground states in AdS ₄ × S ⁷ supergravity. BPS black holes exist only when the conserved charges satisfy a certain non-linear constraint. For other charge sectors, we propose two component configurations comprised of a core black hole that carries macroscopic entropy, and a “gas” that carries a macroscopic fraction of the charge. The superconformal index counts ground states only modulo a linear constraint on the charges. Each index line includes a pure BPS black hole but we find that, when differences between R-charge exceed a certain threshold, the index is dominated by a two component configuration. We illuminate this result by studying the gravitational path integral in Euclidean signature, as function of supersymmetric boundary conditions. We find that a pure BPS black hole saddle dominates the index when the R-charges are comparable, but not when they differ sufficiently. The region where the Euclidean path integral becomes unstable is precisely where two component configurations dominate the index. We show that the KSW criteria are insensitive to this instability.

A bstract: The Euclidean Gravitational Path Integral has proven remarkably effective in the quantum regime of black hole physics. In this work, we examine the applicability of the Kontsevich-Segal-Witten (KSW) criterion for admissible complex metrics in the context of the Euclidean Gravitational Path Integral. We find that, for the super-conformal index of 𝒩 = 4 SYM with unequal angular momenta, the black hole saddle points violate the KSW criterion precisely where the statistical description of the index breaks down. The corresponding critical point coincides with a phase transition into two-component “grey galaxy” configurations.

Supersymmetric AdS black hole solutions exist only when their angular momenta and charges satisfy a certain constraint that depends on the dimension. We show that these nonlinear relations on the conserved charges agree with a computation in the dual supersymmetric CFT in its free limit, with interactions entering only through a uniform rescaling of all charges. Our computations apply to the highly non-trivial charge constraints for AdS₄, AdS₅ and AdS₇ black holes, and generalize an earlier one for the analogous constraint in AdS₃. Our results suggest a microscopic understanding of AdS black holes beyond the scope of supersymmetric indices.

We discuss AdS₂ quantum gravity from an unconventional perspective that emphasizes bulk geometry. In our approach, AdS₂ has no boundary, there are no divergences that require renormalization, and the dilaton of JT-gravity can be omitted altogether. The result is the standard Schwarzian theory. However, it may be advantageous that our derivation just relies on conventional AdS/CFT correspondence and effective quantum field theory. For example, it clarifies the symmetry breaking pattern. It also puts the non-compact AdS₂ topology on the same footing as compact Riemann surfaces.

Motivated by recent studies of supersymmetric black holes, we revisit the phase diagram of AdS black holes, whether BPS or not, with particular emphasis on the role of rotation. We develop BPS thermodynamics systematically and, in many explicit examples, we study its striking similarities with more familiar AdS black holes, as well as some differences. We highlight an important fugacity that preserves BPS saturation but is not captured by the supersymmetric index.