Black Hole Microstates and Attractor Without Supersymmetry

TL;DR

This work extends the attractor mechanism beyond supersymmetry to extremal black holes, arguing that macroscopic entropy remains independent of asymptotic moduli and should coincide with weak-coupling microscopic counts across coupling regimes. Using the entropy-function formalism and AdS2 (and, when available, AdS3) near-horizon analyses, the authors demonstrate multiple nonsupersymmetric examples where $S_{BH}$ and $S_{stat}$ agree to leading order, and discuss caveats such as flat-direction lifting and runaways that can be tamed by slight non-extremality. The paper also clarifies the definitions of microscopic entropy for non-BPS states and contrasts AdS2- vs AdS3-based approaches, highlighting when each method provides robust non-renormalization results. Overall, the results offer a broad, conjectural framework for relating strong-coupling black hole entropy to weak-coupling microstate counting in non-supersymmetric settings, with implications for holography and string dualities.

Abstract

Due to the attractor mechanism, the entropy of an extremal black hole does not vary continuously as we vary the asymptotic values of various moduli fields. Using this fact we argue that the entropy of an extremal black hole in string theory, calculated for a range of values of the asymptotic moduli for which the microscopic theory is strongly coupled, should match the statistical entropy of the same system calculated for a range of values of the asymptotic moduli for which the microscopic theory is weakly coupled. This argument does not rely on supersymmetry and applies equally well to nonsupersymmetric extremal black holes. We discuss several examples which support this argument and also several caveats which could invalidate this argument.