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

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

Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs

“…For non-zero rank case, the resulting non-unitary TQFTs are non-semisimple and thus are not genuine TQFTs satisfying Atiyah's axioms. Understanding mathematical structures of the generalized notion of TQFTs and its relation to 3D SCFTs are currently active research area [3][4][5].…”