Vertex operator algebras and topologically twisted Chern-Simons-matter theories
Niklas Garner
Abstract
A bstract 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 Chern-Simons-matter theories of Gaiotto-Witten, but we show that there is a topological “ A -twist” for a much larger class of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> ≠ 4 theories. We illustrate a particular example of this new class of theories that admits the p = 2 singlet VOA $$ \mathfrak{M} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> </mml:math> (2) on its boundary and comment on its relation to the ψ → ∞ limit of the Gaiotto-Rapčák corner VOA Y 1 , 1 , 0 [ ψ ].