Journal of High Energy Physics

, 2013:168 | Cite as

ABJM Wilson loops in arbitrary representations

  • Yasuyuki Hatsuda
  • Masazumi HondaEmail author
  • Sanefumi Moriyama
  • Kazumi Okuyama
Open Access


We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.


Matrix Models Wilson ’t Hooft and Polyakov loops Topological Strings M-Theory 


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Copyright information

© SISSA 2013

Authors and Affiliations

  • Yasuyuki Hatsuda
    • 1
    • 2
  • Masazumi Honda
    • 3
    • 4
    Email author
  • Sanefumi Moriyama
    • 4
    • 5
  • Kazumi Okuyama
    • 6
  1. 1.DESY Theory Group, DESY HamburgHamburgGermany
  2. 2.Department of PhysicsTokyo Institute of TechnologyMeguro-kuJapan
  3. 3.High Energy Accelerator Research Organization (KEK)TsukubaJapan
  4. 4.Yukawa Institute for Theoretical PhysicsKyoto UniversitySakyo-kuJapan
  5. 5.Kobayashi Maskawa Institute and Graduate School of MathematicsNagoyaJapan
  6. 6.Department of PhysicsShinshu UniversityMatsumotoJapan

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