Coulomb Branch Operators and Mirror Symmetry in Three Dimensions

Understand

We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in three-dimensional $\mathcal{N} = 4$ abelian gauge theories that have superconformal infrared limits.

• These operators are position-dependent linear combinations of Coulomb branch operators.
• They form a one-dimensional topological sector that encodes a deformation quantization of the Coulomb branch chiral ring, and their correlation functions completely fix the ($n\leq 3$)-point functions of all half-BPS Coulomb branch operators.
• Using these results, we provide new derivations of the conformal dimension of half-BPS monopole operators as well as new and detailed tests of mirror symmetry.