BPS Black Holes in AdS4 from M-theory

TL;DR

The paper constructs and analyzes supersymmetric, asymptotically $AdS_4$ black holes in ${ m N}=2$ gauged supergravity with hypermultiplets, realized as consistent M-theory reductions on Sasaki–Einstein seven-manifolds. It derives general BPS flow equations for electrically gauged theories and the horizon (attractor-like) fixed-point relations, then applies them to multiple truncations ${ m Q}^{111},{ m M}^{111},{ m N}^{11}$, the squashed $S^7$, and ${ m SU}(4)/{ m SU}(3)$, uncovering a four-parameter horizon space for ${ m Q}^{111}$ and truncated subspaces for the others. The authors construct explicit numerical black-hole solutions interpolating between $AdS_4$ and $AdS_2 imes ext{S}^2$, including a ${ m Q}^{111}$-based solution matching prior eleven-dimensional results, and a richer ${ m M}^{111}$ case with running hypermultiplet scalars. These results illuminate how hypermultiplets shape BPS flows and horizon geography, and they connect four-dimensional black holes to wrapped M2/M5-brane configurations in M-theory with potential holographic applications to twisted three-dimensional Chern–Simons matter theories. The work advances understanding of horizon attractors in gauged supergravity with hypermultiplets and provides a concrete framework for exploring holographic states dual to M2-brane configurations on complex internal geometries.

Abstract

We study supersymmetric black holes in $AdS_4$ in the framework of four dimensional gauged $\N=2$ supergravity coupled to hypermultiplets. We derive the flow equations for a general electrically gauged theory where the gauge group is Abelian and, restricting them to the fixed points, we derive the gauged supergravity analogue of the attractor equations for theories coupled to hypermultiplets. The particular models we analyze are consistent truncations of M-theory on certain Sasaki-Einstein seven-manifolds. We study the space of horizon solutions of the form $AdS_2\times Σ_g$ with both electric and magnetic charges and find a four-dimensional solution space when the theory arises from a reduction on $Q^{111}$. For other $SE_7$ reductions, the solutions space is a subspace of this. We construct explicit examples of spherically symmetric black holes numerically.

Figures (2)

• Figure 1: Plots of $u',v'$ and $\rho$ on the left and of $e_1,e_2$ and $b_1/2$ on the right corresponding to the IR parameters $c_1=-1.208,c_2=0.989,c_3=-0.974$ and the UV parameters $\beta_1=-2.08,\epsilon_1=-1.325, \epsilon_4=5$.
• Figure 2: Plots of $u',v', (2 b_1+b_2)/3,\rho$ on the left and of $(b_2-b_1)/3, e_1,e_2,\pi-\psi$ on the right corresponding to the value $c_1=1.7086,c_2=-2.4245,c_3=0.6713,c_4=-3.7021$. The UV expansion will be matched up to the transformations (\ref{['simm1']}) and (\ref{['simm2']}).