Vortices and Vermas

Understand

In three-dimensional gauge theories, monopole operators create and destroy vortices.

• We explore this idea in the context of 3d N=4 gauge theories in the presence of an Omega-background.
• In this case, monopole operators generate a non-commutative algebra that quantizes the Coulomb-branch chiral ring.
• The monopole operators act naturally on a Hilbert space, which is realized concretely as the equivariant cohomology of a moduli space of vortices.