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Coulomb branch operators and mirror symmetry in three dimensions

Author(s): Dedushenko, Mykola; Fam, Yale; Pufu, Silviu S; Yacoby, Ran

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Abstract: 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 S-3 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.
Publication Date: Apr-2018
Electronic Publication Date: 9-Apr-2018
Citation: Dedushenko, Mykola, Fam, Yale, Pufu, Silviu S, Yacoby, Ran. (2018). Coulomb branch operators and mirror symmetry in three dimensions. JOURNAL OF HIGH ENERGY PHYSICS, 10.1007/JHEP04(2018)037
DOI: doi:10.1007/JHEP04(2018)037
ISSN: 1029-8479
Type of Material: Journal Article
Version: Final published version. This is an open access article.

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