Vertex Operator Algebras and Topologically Twisted Chern-Simons-Matter Theories

TL;DR

This paper explores boundary vertex operator algebras (VOAs) in topologically twisted Chern-Simons-matter theories, linking them to line operator categories and introducing new classes of theories with specific VOAs like the singlet VOA.

Contribution

It proposes boundary VOAs for a broad class of topologically twisted theories, extending the known examples from Gaiotto-Witten models and identifying new boundary VOAs such as the singlet VOA.

Findings

Boundary VOAs model line operator categories in 3d theories.

Existence of a topological A-twist for a wider class of theories.

Identification of the singlet VOA $rak{M}(2)$ in a new theory example.

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 $\mathcal{N}=4$ 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 $Y_{1,1,0}[\psi]$.