2024/08/18 by Ki Fung Chan, Naichung Conan Leung, Chan, Ki Fung +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #Symplectic Geometry (math.SG) #math.AG #math.RT #math.SG
paper · pdf · doi:10.48550/arxiv.2408.09479
27 pages. Substantially revised and expanded version: added new results and theorems, expanded the exposition and proofs
arxiv created 2026/07/31 · arxiv updated 2026/08/03
We establish a connection between (nonabelian) equivariant 2d mirror symmetry and the geometry of Coulomb branches. In the context of 3d mirror symmetry, a Hamiltonian G-manifold Y is expected to determine a complex Lagrangian subvariety \mathbbLGY of the Coulomb branch. Using transverse Hilbert schemes and nil-Hecke algebras, we develop an algebro-geometric framework for studying Coulomb branches and their Lagrangian subvarieties and formulate criteria for the existence of \mathbbLGY in terms of equivariant 2d mirror symmetry. We then reinterpret these criteria in terms of Lagrangian displaceability and prove the resulting statements using Lagrangian Floer theory.