ABJM to BMN in a Double Scale Limit: Indices and Bubbling Geometries

We study a double scale limit of $U(N)_k\times U(N)_{-k}$ ABJM theory, with $N,k\to\infty$ and $N/k^2\toν\in(0,\infty)$, at fixed positive total monopole charge $q$. In this limit, the Penrose geometry retains a compact null circle of finite radius, and the sector of monopole charge $q$ carries $q$