Wilson loops and its correlators with chiral operators in \( \mathcal{N} \) = 2, 4 SCFT at large N

  • E. SysoevaEmail author
Open Access
Regular Article - Theoretical Physics


In this paper we compute the vacuum expectation value of the Wilson loop and its correlators with chiral primary operators in \( \mathcal{N} \) = 2, 4 superconformal U(N ) gauge theories at large N . After localization these quantities can be computed in terms of a deformed U(N ) matrix model. The Wilson loops we deal with are in the fundamental and symmetric representations.


1/N Expansion Matrix Models Supersymmetric Gauge Theory Wilson ’t Hooft and Polyakov loops 


Open Access

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  1. [1]
    J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    J.K. Erickson, G.W. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    E. Brézin, C. Itzykson, G. Parisi and J.B. Zuber, Planar diagrams, Commun. Math. Phys. 59 (1978) 35 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    P. Di Francesco, P.H. Ginsparg and J. Zinn-Justin, 2D gravity and random matrices, Phys. Rept. 254 (1995) 1 [hep-th/9306153] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The operator product expansion for Wilson loops and surfaces in the large N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    G.W. Semenoff and K. Zarembo, More exact predictions of SUSYM for string theory, Nucl. Phys. B 616 (2001) 34 [hep-th/0106015] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    S. Giombi, R. Ricci and D. Trancanelli, Operator product expansion of higher rank Wilson loops from D-branes and matrix models, JHEP 10 (2006) 045 [hep-th/0608077] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    F. Fucito, J.F. Morales and R. Poghossian, Wilson loops and chiral correlators on squashed spheres, JHEP 11 (2015) 064 [arXiv:1507.05426] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    M. Billó et al., Two-point correlators in N = 2 gauge theories, Nucl. Phys. B 926 (2018) 427 [arXiv:1705.02909] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    E. Gerchkovitz et al., Correlation functions of Coulomb branch operators, JHEP 01 (2017) 103.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    K. Okuyama and G.W. Semenoff, Wilson loops in N = 4 SYM and fermion droplets, JHEP 06 (2006) 057 [hep-th/0604209] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    D. Rodriguez-Gomez and J.G. Russo, Operator mixing in large N superconformal field theories on S 4 and correlators with Wilson loops, JHEP 12 (2016) 120 [arXiv:1607.07878] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    N. Halmagyi and T. Okuda, Bubbling Calabi-Yau geometry from matrix models, JHEP 03 (2008) 028 [arXiv:0711.1870] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    T. Okuda and D. Trancanelli, Spectral curves, emergent geometry and bubbling solutions for Wilson loops, JHEP 09 (2008) 050 [arXiv:0806.4191] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    J.F. Morales, F. Fucito and E. Sysoeva, Wilson loop and its correlators in the limit of large coupling constant, arXiv:1803.00649.
  17. [17]
    N. Drukker and D.J. Gross, An exact prediction of N = 4 SUSYM theory for string theory, J. Math. Phys. 42 (2001) 2896 [hep-th/0010274] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    S.K. Lando and A.K. Zvonkin, Graphs on surfaces and their applications, Encyclopaedia of Mathematical Sciences, Springer, Germany (2004).Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Diparimento di FisicaUniversità di Roma Tor Vergata, and INFN — Sezione di Roma Tor VergataRomaItaly

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