The 3d $$ \mathcal{N} $$ = 6 bootstrap: from higher spins to strings to membranes

We study the space of 3d ${\cal N} = 6$ SCFTs by combining numerical bootstrap techniques with exact results derived using supersymmetric localization. First we derive superconformal block decomposition four-point function stress tensor multiplet primary. then use localization for $U(N)_k\times U(N+M)_{-k}$ Chern-Simons-matter theories to determine two protected OPE coefficients many values $N,M,k$. These inputs are combined compute precise rigorous islands a wide range $N,k$ at $M=0$, so that can non-perturbatively interpolate between M-theory duals small $k$ and string theory large $k$. also present evidence $U(1)_{2M}\times U(1+M)_{-2M}$ theory, which has vector-like large-$M$ limit dual higher spin saturates bounds certain CFT data. The extremal functional allows us conjecturally reconstruct low-lying data this theory.