Coulomb branch algebras via symplectic cohomology

Let ( ¯ M,ω) be a compact symplectic manifold with convex boundary and c1(T ¯ 0. Suppose that ( ¯ M)= M,ω) 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 Gequivariant symplectic cohomology of ¯ M. Building on work of Teleman [T2], we use this construction to characterize the Coulomb branches of Braverman-Finkelberg-Nakajima [BFN1] in terms of equivariant symplectic cohomology.