Spectrum of BPS black holes in $AdS_3 \times S^3 \times S^3 \times S^1$

Abstract

We uncover novel features in the spectrum of BPS and near-BPS states in asymptotically $AdS_3 \times S^3 \times S^3 \times S^1$ spacetimes. This follows from a careful analysis of semiclassical and quantum black holes in this theory, which have peculiarities due to the nonlinear large $\mathcal{N}=4$ superconformal symmetry. Notably, we find that the $S^3 \times S^3$ angular momentum spectrum of BPS states in the Ramond sector exhibits discrete jumps as a function of the ratio between the radii of the two three-spheres. This phenomenon is a quantum gravity effect for which no microscopic derivation is currently known. In addition, we construct a family of non-extremal supersymmetric black holes that contribute to a supersymmetric index yet possess a temperature-dependent free energy. Analogous results apply to six-dimensional black holes with $AdS_2 \times S^2 \times S^2$ near-horizon geometries constructed in M-theory compactifications.