The Perturbation Spectrum of Black Holes in N=8 Supergravity

TL;DR

The work computes and organizes the perturbation spectrum of $N=8$ black holes in both four and five dimensions within the dilute gas regime, exploiting the near-horizon geometry $AdS_3\times S^2$ (and $AdS_3\times S^3$ for 5D) and the associated global and superconformal symmetries. It provides a group-theoretical construction of the spectrum, identifies the relevant supermultiplets, and derives the leading conformal weights and chiral primary fields, including a detailed 4D/$N=8$ analysis and an explicit 5D decoupling of equations of motion. The results are interpreted microscopically in terms of intersecting M5-branes in 4D and D1–D5 configurations on a small torus in 5D, and compared to the dual string theories, highlighting agreements and subtle discrepancies such as gauge-mode decouplings and a stringy exclusion principle. Together, these findings advance the understanding of black hole dynamics in AdS/CFT and offer concrete predictions for the corresponding two-dimensional CFTs and their chiral primaries.

Abstract

The near horizon geometry of four-dimensional black holes in the dilute gas regime is AdS_3 x S^2, and the global symmetry group is SU(2) x USp(6). This is exploited to calculate their perturbation spectrum using group theoretical methods. The result is interpreted in terms of three extreme M5-branes, orthogonally intersecting over a common string. We also consider N=8 black holes in five dimensions, and compute the spectrum by explicit decoupling of the equations of motion, extending recent work on N=4 black holes. This result is interpreted in terms of D1- and D5-branes that are wrapped on a small four-torus. The spectra are compared with string theory.