Advertisement

Linear Chern-Simons-matter theories in the planar limit

  • Takao SuyamaEmail author
Open Access
Regular Article - Theoretical Physics
  • 25 Downloads

Abstract

We study \( \mathcal{N} \) = 3 linear Chern-Simons-matter theories in the planar limit. The matter content of the theory is depicted by a linear-shape diagram with n nodes and n − 1 links for any n. The free energy and the vevs of BPS Wilson loops are given in terms of a single 1-form on ℂℙ1 which can be determined explicitly for all linear theories. The analytic structure of the vevs of the Wilson loops is investigated in detail for n = 1 and n = 2. Theadditionoffundamentalmattersisalsodiscussed.

Keywords

Matrix Models AdS-CFT Correspondence Chern-Simons Theories 

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

References

  1. [1]
    A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    T. Kitao, K. Ohta and N. Ohta, Three-dimensional gauge dynamics from brane configurations with (p,q)-fivebrane, Nucl. Phys. B 539 (1999) 79 [hep-th/9808111] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    O. Bergman, A. Hanany, A. Karch and B. Kol, Branes and supersymmetry breaking in three-dimensional gauge theories, JHEP 10 (1999) 036 [hep-th/9908075] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  4. [4]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Y. Imamura and K. Kimura, On the moduli space of elliptic Maxwell-Chern-Simons theories, Prog. Theor. Phys. 120 (2008) 509 [arXiv:0806.3727] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  6. [6]
    D.L. Jafferis and A. Tomasiello, A simple class of N = 3 gauge/gravity duals, JHEP 10 (2008) 101 [arXiv:0808.0864] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    D. Gaiotto and E. Witten, Janus Configurations, Chern-Simons Couplings, And The θ-Angle in N = 4 Super Yang-Mills Theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets, JHEP 07 (2008) 091 [arXiv:0805.3662] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    T. Nosaka and S. Yokoyama, Complete factorization in minimal \( \mathcal{N} \) = 4 Chern-Simons-matter theory, JHEP 01 (2018) 001 [arXiv:1706.07234] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  11. [11]
    T. Nosaka and S. Yokoyama, Index and duality of minimal \( \mathcal{N} \) = 4 Chern-Simons-matter theories, JHEP 06 (2018) 028 [arXiv:1804.04639] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  12. [12]
    D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-Matter theories, JHEP 08 (2007) 056 [arXiv:0704.3740] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    N. Drukker and D. Trancanelli, A supermatrix model for N = 6 super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    H. Ouyang, J.-B. Wu and J.-j. Zhang, Construction and classification of novel BPS Wilson loops in quiver Chern-Simons-matter theories, Nucl. Phys. B 910 (2016) 496 [arXiv:1511.02967] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    J. Cookmeyer, J.T. Liu and L.A. Pando Zayas, Higher Rank ABJM Wilson Loops from Matrix Models, JHEP 11 (2016) 121 [arXiv:1609.08165] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    T. Morita and K. Sugiyama, Multi-cut solutions in Chern-Simons matrix models, Nucl. Phys. B 929 (2018) 1 [arXiv:1704.08675] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    T. Suyama, Notes on Planar Resolvents of Chern-Simons-matter Matrix Models, JHEP 11 (2016) 049 [arXiv:1605.09110] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    T. Suyama, Strong Coupling Limit of A Family of Chern-Simons-matter Theories, JHEP 01 (2018) 125 [arXiv:1706.08204] [INSPIRE].
  19. [19]
    E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    K. Ohta, Supersymmetric index and s rule for type IIB branes, JHEP 10 (1999) 006 [hep-th/9908120] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    D. Gaiotto and E. Witten, S-duality of Boundary Conditions In N = 4 Super Yang-Mills Theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    T. Suyama, Supersymmetry Breaking and Planar Free Energy in Chern-Simons-matter Theories, arXiv:1405.7469 [INSPIRE].
  23. [23]
    T. Morita and V. Niarchos, F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories, Nucl. Phys. B 858 (2012) 84 [arXiv:1108.4963] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306 (2011) 511 [arXiv:1007.3837] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    T. Suyama, A Systematic Study on Matrix Models for Chern-Simons-matter Theories, Nucl. Phys. B 874 (2013) 528 [arXiv:1304.7831] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
  27. [27]
    C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Multi-Matrix Models and Tri-Sasaki Einstein Spaces, Phys. Rev. B 83 (2011) 046001 [arXiv:1011.5487] [INSPIRE].ADSGoogle Scholar
  28. [28]
    D.R. Gulotta, C.P. Herzog and T. Nishioka, The ABCDEF’s of Matrix Models for Supersymmetric Chern-Simons Theories, JHEP 04 (2012) 138 [arXiv:1201.6360] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    M. Mariño and P. Putrov, Exact Results in ABJM Theory from Topological Strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.KEK Theory CenterHigh Energy Accelerator Research Organization (KEK)TsukubaJapan

Personalised recommendations