Dressed AdS$_4$ black holes in M-theory from the 3d superconformal index

Abstract

The superconformal index of 4d $\mathcal N\,{=}\,4$ SYM has been shown to exhibit a rich phase structure, whose holographic interpretation in AdS$_5$ involves (dual-)dressed black holes, gray galaxies, and graviton gas contributions. Here we extend the analysis to 3d CFTs, focusing on ABJM theory and the $\mathcal N=4$ ADHM theory. We study the microcanonical superconformal index with two independent charges at finite $N$ and obtain exact signed state degeneracies up to large charges. The results exhibit the black hole physics expected to emerge at large-$N$, including isolated black holes and black holes dressed by additional matter.