We consider several topologically twisted Chern-Simons-matter theories and propose boundary VOAs whose module categories should model the category of line operators of the 3d bulk. Our main examples come from the topological $A$ and $B$ twists of the exotic $\mathcal{ N}=4$ Chern-Simons-matter theories of Gaiotto-Witten, but we show that there is a topological "$A$-twist" for a much larger class of $\mathcal{ N}\neq4$ theories. We illustrate a particular example of this new class of theories that admits the $p=2$ singlet VOA $\mathfrak{ M}(2)$ on its boundary and comment on its relation to the $\psi \to \infty$ limit of the Gaiotto-Rap{ \v c}{ \'a}k corner VOA $Y_{ 1,1,0}[\psi]$.
Categories: hep-th math.QA