Black Hole Spectroscopy and AdS$_2$ Holography

TL;DR

The work computes the full spectrum of quadratic fluctuations around extremal nonBPS AdS$_2\times S^2$ black hole horizons in ${\cal N}=8$ and ${\cal N}=4$ supergravity, revealing that all conformal weights $h$ are integral despite complete supersymmetry breaking. By performing a detailed partial-wave analysis on $S^2$, dualizing AdS$_2$ vectors, and exploiting symmetry-based block decoupling, the authors obtain a comprehensive bulk and boundary-mode mass spectrum that is consistent with nAdS$_2$/nCFT$_1$ expectations and with dimensional reductions from AdS$_3$/CFT$_2$. They validate the spectrum by computing logarithmic corrections to the extremal entropy and matching previous methods, and they elucidate the connection to AdS$_3\times S^2$ via a nearly null reduction (nNull), clarifying the BPS and nonBPS branches. The results point to a protected-like structure in the nonBPS spectrum and provide a concrete framework for understanding quantum corrections and UV completions of extremal black holes in string theory, including the role of global supersymmetry in organizing states.

Abstract

We compute the spectrum of extremal nonBPS black holes in four dimensions by studying supergravity on their AdS$_2\times S^2$ near horizon geometry. We find that the spectrum exhibits significant simplifications even though supersymmetry is completely broken. We interpret our results in the framework of nAdS$_2$/nCFT$_1$ correspondence and by comparing with dimensional reduction from AdS$_3$/CFT$_2$ duality. As an additional test we compute quantum corrections to extremal black hole entropy on the nonBPS branch and recover results previously determined using very different methods.