A quantum mechanics for magnetic horizons
Francesco Benini, Saman Soltani, Ziruo Zhang
Abstract
A bstract We construct an $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 × 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.