We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in three-dimensional 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 ≤ 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. Our main approach involves supersymmetric localization on a hemisphere HS3 with half-BPS boundary conditions, where operator insertions within the hemisphere are represented by certain shift operators acting on the HS3 wavefunction. By gluing a pair of such wavefunctions, we obtain correlators on S3 with an arbitrary number of operator insertions. Finally, we show that our results can be recovered by dimensionally reducing the Schur index of 4D N= 2 theories decorated by BPS ’t Hooft-Wilson loops.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- Conformal Field Theory
- Extended Supersymmetry
- Supersymmetric Gauge Theory
- Supersymmetry and Duality