Abstract: I will show how supersymmetric localization can be used to calculate correlation functions of half-BPS local operators in 3d N=4 superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The operators primarily studied are certain linear combinations of Higgs branch operators inserted anywhere along a line. These operators are constructed from the hypermultiplet scalars. They form a 1d non-commutative operator algebra with topological correlation functions. The 2- and 3-point functions of Higgs branch operators in the full 3d N=4 theory can be simply inferred from the 1d topological algebra. After conformally mapping the 3d superconformal field theory from flat space to a round three-sphere, supersymmetric localization is performed using a supercharge that does not belong to any 3d N=2 subalgebra of the N=4 algebra. The result is a simple model that can be used to calculate correlation functions in the 1d topological algebra mentioned above. This model is a 1d Gaussian theory coupled to a matrix model, and it can be viewed as a gauge-fixed version of a topological gauged quantum mechanics. These results generalize to non-conformal theories on S3 that contain real mass and Fayet-Iliopolous parameters. I will also provide partial results for the 1d topological algebra associated with the Coulomb branch, where correlators of operators built from the vectormultiplet scalars will be considered.
