Anti-de Sitter Black Holes in Gauged N=8 Supergravity

TL;DR

This work constructs and analyzes AdS$_4$ black holes in gauged $N=8$ supergravity with $SO(8)$ gauging by truncating to the abelian $U(1)^4$ sector, yielding explicit single- and multi-charge solutions. It shows a half-BPS $a=\sqrt{3}$ AdS black hole and a four-charge family preserving fractions $\tfrac{1}{2}$, $\tfrac{1}{4}$, $\tfrac{1}{8}$, and $\tfrac{1}{8}$, along with non-extremal generalizations and magnetic counterparts that are non-BPS for $g\neq0$. A key insight is the conjectured identification of a subset of extremal electric AdS black holes with the $S^7$ Kaluza-Klein spectrum, with non-Abelian $SO(8)$ quantum numbers supplied by fermionic zero modes, linking four-dimensional AdS black holes to higher-dimensional KK physics. The paper also emphasizes the absence of static multi-center solutions in AdS, the impact of gauging on dualities, and the nuanced relation between $g\to0$ limits and the $T^7$ massless sector, suggesting a broader M-theory interpretation via the D=11 supermembrane.

Abstract

We present new anti-de Sitter black hole solutions of gauged N=8, SO(8) supergravity, which is the massless sector of the AdS_4\times S^7 vacuum of M-theory. By focusing on the U(1)^4 Cartan subgroup, we find non-extremal 1, 2, 3 and 4 charge solutions. In the extremal limit, they may preserve up to 1/2, 1/4, 1/8 and 1/8 of the supersymmetry, respectively. In the limit of vanishing SO(8) coupling constant, the solutions reduce to the familiar black holes of the M_4\times T^7 vacuum, but have very different interpretation since there are no winding states on S^7 and no U-duality. In contrast to the T^7 compactification, moreover, we find no static multi-center solutions. Also in contrast, the S^7 fields appear "already dualized" so that the 4 charges may be all electric or all magnetic rather than 2 electric and 2 magnetic. Curiously, however, the magnetic solutions preserve no supersymmetries. We conjecture that a subset of the extreme electric black holes preserving 1/2 the supersymmetry may be identified with the S^7 Kaluza-Klein spectrum, with the non-abelian SO(8) quantum numbers provided by the fermionic zero modes.