Coulomb branch algebras via symplectic cohomology

TL;DR

This paper constructs an action of the Coulomb branch on the equivariant symplectic cohomology of certain symplectic manifolds, linking geometric representation theory with symplectic topology.

Contribution

It introduces a novel construction of Coulomb branch actions on symplectic cohomology and characterizes Coulomb branches via equivariant symplectic cohomology.

Findings

Coulomb branch acts on G-equivariant symplectic cohomology

Characterization of Coulomb branches using symplectic cohomology

Extension of Teleman's work to new geometric settings

Abstract

Let $(\bar{M}, \omega)$ be a compact symplectic manifold with convex boundary and $c_1(T\bar{M})=0$. Suppose that $(\bar{M}, \omega)$ is equipped with a convex Hamiltonian $G$-action for some connected, compact Lie group $G$. We construct an action of the pure Coulomb branch of $G$ on the $G$-equivariant symplectic cohomology of $\bar{M}.$ Building on work of Teleman, we use this construction to characterize the Coulomb branches of Braverman-Finkelberg-Nakajima in terms of equivariant symplectic cohomology.