Vertex operator algebras and topologically twisted Chern-Simons-matter theories

Abstract

Abstract 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 $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N ≠ 4 theories. We illustrate a particular example of this new class of theories that admits the p = 2 singlet VOA $$ \mathfrak{M} $$ M (2) on its boundary and comment on its relation to the ψ → ∞ limit of the Gaiotto-Rapčák corner VOA Y1,1,0[ψ].