3D mirror symmetry is a duality between topological twists of 3-dimensional supersymmetric quantum field theories. One manifestation of this duality is an isomorphism between branches of the moduli space of vacua of mirror theories. These branches, called the Higgs branch and Coulomb branch, are hyperkahler manifolds and the duality between them was studied independently by mathematicians under the guise of « symplectic duality ». In this talk, I will discuss work towards proving these isomorphisms using boundary vertex operator algebras (VOAs). These VOAs are defined on 2-dimensional boundary conditions of the twisted theories and it is conjectured that they contain the data of both the Higgs and Coulomb branches. This conjecture implies a number of duality properties for VOAs appearing in this manner. In particular, I will discuss joint work with Andrea Ferrari in which we prove the Higgs branch conjecture for 3D supers quantum electrodynamics..

https://indico.math.cnrs.fr/event/15105/