A one-dimensional theory for Higgs branch operators

  • Mykola Dedushenko
  • Silviu S. Pufu
  • Ran Yacoby
Open Access
Regular Article - Theoretical Physics


We use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3d \( \mathcal{N}=4 \) superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The operators we primarily study are certain twisted linear combinations of Higgs branch operators that can be inserted anywhere along a given line. These operators are constructed from the hypermultiplet scalars. They form a one-dimensional non-commutative operator algebra with topological correlation functions. The 2- and 3-point functions of Higgs branch operators in the full 3d \( \mathcal{N}=4 \) theory can be simply inferred from the 1d topological algebra. After conformally mapping the 3d superconformal field theory from flat space to a round three-sphere, we preform supersymmetric localization using a supercharge that does not belong to any 3d \( \mathcal{N}=2 \) subalgebra of the \( \mathcal{N}=4 \) algebra. The result is a simple model that can be used to calculate correlation functions in the 1d topological algebra mentioned above. This model is a 1d Gaussian theory coupled to a matrix model, and it can be viewed as a gauge-fixed version of a topological gauged quantum mechanics. Our results generalize to non-conformal theories on S3 that contain real mass and Fayet-Iliopolous parameters. We also provide partial results in the 1d topological algebra associated with the Coulomb branch, where we calculate correlation functions of local operators built from the vectormultiplet scalars.


Extended Supersymmetry Supersymmetric Gauge Theory Conformal Field Theory 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Mykola Dedushenko
    • 1
    • 2
  • Silviu S. Pufu
    • 1
  • Ran Yacoby
    • 1
    • 3
  1. 1.Joseph Henry LaboratoriesPrinceton UniversityPrincetonU.S.A.
  2. 2.Walter Burke Institute for Theoretical PhysicsCalifornia Institute of TechnologyPasadenaU.S.A.
  3. 3.Department of Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael

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