Higgs and Coulomb branches from vertex operator algebras
Kevin Costello (Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada); Thomas Creutzig (Department of Mathematics, University of Alberta, Edmonton, AB, T6G 2G1, Canada); Davide Gaiotto (Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada)
We formulate a conjectural relation between the category of line defects in topologically twisted 3d $$ \mathcal{N} $$ = 4 supersymmetric quantum field theories and categories of modules for Vertex Operator Algebras of boundary local operators for the theories. We test the conjecture in several examples and provide some partial proofs for standard classes of gauge theories.