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Journal of High Energy Physics

, 2016:9 | Cite as

The quantum 1/2 BPS Wilson loop in \( \mathcal{N}=4 \) Chern-Simons-matter theories

  • Marco S. Bianchi
  • Luca Griguolo
  • Matias Leoni
  • Andrea Mauri
  • Silvia Penati
  • Domenico Seminara
Open Access
Regular Article - Theoretical Physics

Abstract

In three dimensional \( \mathcal{N}=4 \) Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level. We compute their three-loop expectation value in a convenient color sector and prove that the degeneracy is uplifted by quantum corrections. We expand the matrix model prediction in the same regime and by comparison we conclude that the quantum 1/2 BPS Wilson loop is the average of the two operators. We provide an all-loop argument to support this claim at any order. As a by-product, we identify the localization result at three loops as a correction to the framing factor induced by matter interactions. Finally, we comment on the quantum properties of the non-1/2 BPS Wilson loop operator defined as the difference of the two fermionic ones.

Keywords

Chern-Simons Theories Matrix Models Wilson, ’t Hooft and Polyakov loops 

Notes

Open Access

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.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Marco S. Bianchi
    • 1
  • Luca Griguolo
    • 2
  • Matias Leoni
    • 3
  • Andrea Mauri
    • 4
  • Silvia Penati
    • 4
    • 5
  • Domenico Seminara
    • 6
  1. 1.Center for Research in String Theory, School of Physics and Astronomy Queen Mary University of LondonLondonU.K.
  2. 2.Dipartimento di Fisica e Scienze della Terra, Università di Parma and INFN — Gruppo Collegato di ParmaParmaItaly
  3. 3.Physics Department, FCEyN-UBA & IFIBA-CONICET Ciudad UniversitariaBuenos AiresArgentina
  4. 4.Dipartimento di FisicaUniversità degli studi di Milano-BicoccaMilanoItaly
  5. 5.INFN — Sezione di Milano-BicoccaMilanoItaly
  6. 6.Dipartimento di Fisica, Università di Firenze and INFN — Sezione di FirenzeSesto FiorentinoItaly

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