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Title: Coulomb branch operators and mirror symmetry in three dimensions

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 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 Hooft-Wilson loops.

Authors:
 [1]; ORCiD logo [2];  [2];  [3]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
  2. Princeton Univ., Princeton, NJ (United States). Dept. of Physics
  3. Weizmann Inst. of Science, Rehovot (Israel). Dept. of Particle Physics and Astrophysics
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1499694
Grant/Contract Number:  
SC0011632
Resource 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 1029-8479
Publisher:
Springer Berlin
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

Citation Formats

Dedushenko, Mykola, Fan, Yale, Pufu, Silviu S., and Yacoby, Ran. Coulomb branch operators and mirror symmetry in three dimensions. United States: N. p., 2018. 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. Mon . "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 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. Lastly, 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.},
doi = {10.1007/jhep04(2018)037},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2018,
place = {United States},
year = {2018},
month = {4}
}

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