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Coulomb Branch Operators and Mirror Symmetry in Three Dimensions

Dedushenko, Mykola and Fan, Yale and Pufu, Silviu S. and Yacoby, Ran (2018) Coulomb Branch Operators and Mirror Symmetry in Three Dimensions. Journal of High Energy Physics, 2018 (4). Art. No. 037. ISSN 1126-6708. doi:10.1007/JHEP04(2018)037.

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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 HS^3 with half-BPS 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. 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.

Item Type:Article
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URLURL TypeDescription Paper
Dedushenko, Mykola0000-0002-9273-7602
Pufu, Silviu S.0000-0001-8316-9589
Additional Information:© 2018 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: February 12, 2018; Accepted: March 28, 2018; Published: April 9, 2018. We thank Ofer Aharony, Clay C_ordova, Tudor Dimofte, Bruno Le Floch, Davide Gaiotto, Sergei Gukov, Masazumi Honda, Mikhail Isachenkov, Anton Kapustin, Victor Mikhaylov, Shlomo S. Razamat, Shu-Heng Shao, Genis Torrents, Gustavo J. Turiaci, and Itamar Yaakov for useful discussions. We especially thank Davide Gaiotto for sharing unpublished notes and for a fruitful discussion. While preparing this work, we have benefited from multiple meetings of the Simons Collaboration on the Nonperturbative Bootstrap. The work of MD was supported by the Walter Burke Institute for Theoretical Physics and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, as well as the Sherman Fairchild Foundation. YF gratefully acknowledges support from the NSF GRFP under Grant No. DGE-1656466 and from the Graduate School at Princeton University. The work of SSP was supported in part by the Simons Foundation Grant No. 488651. The work of RY was supported in part by a grant from the Israel Science Foundation Center for Excellence, by the Minerva Foundation with funding from the Federal German Ministry for Education and Research, and by the ISF within the ISF-UGC joint research program framework (grant no. 1200/14).
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Sherman Fairchild FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1656466
Princeton UniversityUNSPECIFIED
Simons Foundation488651
Israel Science FoundationUNSPECIFIED
Minerva FoundationUNSPECIFIED
Bundesministerium für Bildung und Forschung (BMBF)UNSPECIFIED
ISF-UGC joint research program framework1200/14
Subject Keywords:Extended Supersymmetry; Supersymmetric Gauge Theory; Supersymmetry and Duality; Conformal Field Theory
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Issue or Number:4
Record Number:CaltechAUTHORS:20180109-160016229
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Official Citation:Dedushenko, M., Fan, Y., Pufu, S.S. et al. J. High Energ. Phys. (2018) 2018: 37.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84210
Deposited By: Joy Painter
Deposited On:10 Jan 2018 00:13
Last Modified:15 Nov 2021 20:17

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