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Finite $N$ black hole cohomologies
We study new cohomologies for the BPS operators of the $\mathcal{N}=4$ Yang-Mills theory with $SU(3)$ and $SU(4)$ gauge groups, to better understand the black hole microstates. We first study the index of these black hole operators and identify their apparent threshold levels. For $SU(3)$, we find m
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