A quantum mechanics for magnetic horizons

We construct an $\mathcal{N}=2$ supersymmetric gauged quantum mechanics, by starting from the 3d Chern-Simons-matter theory holographically dual to massive Type IIA string theory on AdS${}_4\times S^6$, and Kaluza-Klein reducing on $S^2$ with a background that is dual to the asymptotics of static dyonic BPS black holes in AdS${}_4$. The background involves a choice of gauge fluxes, that we fix via a saddle-point analysis of the 3d topologically twisted index at large $N$. The ground-state degeneracy of the effective quantum mechanics reproduces the entropy of BPS black holes, and we expect its low-lying spectrum to contain information about near-extremal horizons. Interestingly, the model has a large number of statistically-distributed couplings, reminiscent of SYK models.