Two roads to fortuity in ABJM theory

A recently proposed addition to the holographic dictionary connects extremal black holes to fortuitous operators -- those which are only supersymmetric for sufficiently small values of the central charge. The most efficient techniques for finding them come from studying the cohomology of a nilpotent supercharge. We explore two aspects of this problem in weakly-coupled ABJM theory, where the gauge group is $\mathrm{U}(N) \times \mathrm{U}(N)$ and the Chern-Simons level is taken to be large. Adapting an algorithm which has been used to great effect in $\mathcal{N} = 4$ Super Yang-Mills, we enumerate 244 low-lying fortuitous operators and sort them into multiplets of the centralizer algebra. This leads to the construction of two leading fortuitous representatives for $N = 3$ which are subleading for $N = 2$. In the second part of this work, we identify a truncation of ABJM theory where the action of the one-loop supercharge matches the one in the BMN subsector of $\mathcal{N} = 4$ Super Yang-Mills. This allows a known infinite tower of representatives to be lifted from one theory to the other.