Abstract
We introduce two mirror constructions of Vertex Operator Algebras associated to special boundary conditions in 3d mathcal{N} = 4 gauge theories. We conjecture various relations between these boundary VOA’s and properties of the (topologically twisted) bulk theories. We discuss applications to the Symplectic Duality and Geometric Langlands programs.
Highlights
A recurring theme in supersymmetric gauge theory is the discovery of relations to the theory of Vertex Operator Algebras
We introduce two mirror constructions of Vertex Operator Algebras associated to special boundary conditions in 3d N = 4 gauge theories
The idea that VOAs can be embedded into the algebra of local operators in a higherdimensional quantum field theory can be generalized beyond the six-dimensional setting [4]
Summary
A recurring theme in supersymmetric gauge theory is the discovery of relations to the theory of Vertex Operator Algebras. The six-dimensional setup can be mapped to configurations involving junctions of boundary conditions in topologically twisted N = 4 Super Yang Mills [7] In all of these examples, the VOAs live in the physical space of the quantum field theory. The original motivation for introducing these VOAs is that they can provide a powerful computational tool to study the bulk TFT. They may make manifest IR symmetries of the theory, which would be hard to account for with traditional methods [8] but are necessary for certain applications, such as the gauge theory interpretation of the Geometric Langlands program [9,10,11]. Information may flow in the opposite direction, as gauge theory constructions provide a new framework to understand, organize and predict a variety of results in the theory of VOAs [12]
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