Holographic microstate counting for AdS4 black holes in massive IIA supergravity

We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS4 × S 6 from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional N=2 Chern-Simons-matter gauge theories in the large N limit. The I-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic N=2 gauged supergravity, that arises as a consistent truncation of massive type IIA supergravity on S 6. In particular, our results prove that the imaginary part of the three-dimensional partition functions plays a crucial rôle in holography.