TY - JOUR
T1 - Coulomb branch operators and mirror symmetry in three dimensions
AU - Dedushenko, Mykola
AU - Fan, Yale
AU - Pufu, Silviu S.
AU - Yacoby, Ran
N1 - Funding Information:
We thank Ofer Aharony, Clay Córdova, 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 We especially thank Davide Gaiotto for sharing unpublished notes and for a fruitful discussion.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).
Publisher Copyright:
© 2018, The Author(s).
PY - 2018/4/1
Y1 - 2018/4/1
N2 - 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.
AB - 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.
KW - Conformal Field Theory
KW - Extended Supersymmetry
KW - Supersymmetric Gauge Theory
KW - Supersymmetry and Duality
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U2 - 10.1007/JHEP04(2018)037
DO - 10.1007/JHEP04(2018)037
M3 - Article
AN - SCOPUS:85046670362
SN - 1126-6708
VL - 2018
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 4
M1 - 37
ER -