Coulomb branch operators and mirror symmetry in three dimensions
We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in threedimensional N = 4 abelian gauge theories that have superconformal infrared limits. These operators are positiondependent linear combinations of Coulomb branch operators. They form a onedimensional 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 halfBPS Coulomb branch operators. Using these results, we provide new derivations of the conformal dimension of halfBPS monopole operators as well as new and detailed tests of mirror symmetry. Our main approach involves supersymmetric localization on a hemisphere HS ^{3} with halfBPS boundary conditions, where operator insertions within the hemisphere are represented by certain shift operators acting on the HS ^{3} wavefunction. By gluing a pair of such wavefunctions, we obtain correlators on S ^{3} with an arbitrary number of operator insertions. Lastly, we show that our results can be recovered by dimensionally reducing the Schur index of 4D N=2 theories decorated by BPS ’t HooftWilson loops.
 Authors:

^{[1]};
^{[2]}
;
^{[2]};
^{[3]}
 California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
 Princeton Univ., Princeton, NJ (United States). Dept. of Physics
 Weizmann Inst. of Science, Rehovot (Israel). Dept. of Particle Physics and Astrophysics
 Publication Date:
 Grant/Contract Number:
 SC0011632
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 4; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Extended Supersymmetry; Supersymmetric Gauge Theory; Supersymmetry and Duality; Conformal Field Theory
 OSTI Identifier:
 1499694
Dedushenko, Mykola, Fan, Yale, Pufu, Silviu S., and Yacoby, Ran. Coulomb branch operators and mirror symmetry in three dimensions. United States: N. p.,
Web. doi:10.1007/jhep04(2018)037.
Dedushenko, Mykola, Fan, Yale, Pufu, Silviu S., & Yacoby, Ran. Coulomb branch operators and mirror symmetry in three dimensions. United States. doi:10.1007/jhep04(2018)037.
Dedushenko, Mykola, Fan, Yale, Pufu, Silviu S., and Yacoby, Ran. 2018.
"Coulomb branch operators and mirror symmetry in three dimensions". United States.
doi:10.1007/jhep04(2018)037. https://www.osti.gov/servlets/purl/1499694.
@article{osti_1499694,
title = {Coulomb branch operators and mirror symmetry in three dimensions},
author = {Dedushenko, Mykola and Fan, Yale and Pufu, Silviu S. and Yacoby, Ran},
abstractNote = {We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in threedimensional N = 4 abelian gauge theories that have superconformal infrared limits. These operators are positiondependent linear combinations of Coulomb branch operators. They form a onedimensional 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 halfBPS Coulomb branch operators. Using these results, we provide new derivations of the conformal dimension of halfBPS monopole operators as well as new and detailed tests of mirror symmetry. Our main approach involves supersymmetric localization on a hemisphere HS3 with halfBPS 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. Lastly, we show that our results can be recovered by dimensionally reducing the Schur index of 4D N=2 theories decorated by BPS ’t HooftWilson loops.},
doi = {10.1007/jhep04(2018)037},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2018,
place = {United States},
year = {2018},
month = {4}
}