Journal of High Energy Physics

, 2014:165 | Cite as

Large N Chern-Simons with massive fundamental fermions — A model with no bound states

  • Yitzhak Frishman
  • Jacob Sonnenschein
Open Access
Regular Article - Theoretical Physics


In a previous paper [1], we analyzed the theory of massive fermions in the fundamental representation coupled to a U(N ) Chern-Simons gauge theory in three dimensions at level K. It was done in the large N , large K limits where \( \lambda =\frac{N}{K} \) was kept fixed. Among other results, we showed there that there are no high mass “quark anti-quark” bound states. Here we show that there are no bound states at all.


Chern-Simons Theories Field Theories in Lower Dimensions Nonperturbative Effects 


Open Access

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  1. [1]
    Y. Frishman and J. Sonnenschein, Breaking conformal invarianceLarge-N Chern-Simons theory coupled to massive fundamental fermions, JHEP 12 (2013) 091 [arXiv:1306.6465] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S. Giombi, S. Minwalla, S. Prakash, S.P. Trivedi, S.R. Wadia et al., Chern-Simons Theory with Vector Fermion Matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    O. Aharony, S. Giombi, G. Gur-Ari, J. Maldacena and R. Yacoby, The Thermal Free Energy in Large-N Chern-Simons-Matter Theories, JHEP 03 (2013) 121 [arXiv:1211.4843] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    O. Aharony, G. Gur-Ari and R. Yacoby, Correlation Functions of Large-N Chern-Simons-Matter Theories and Bosonization in Three Dimensions, JHEP 12 (2012) 028 [arXiv:1207.4593] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  5. [5]
    O. Aharony, G. Gur-Ari and R. Yacoby, D = 3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  6. [6]
    G. Gur-Ari and R. Yacoby, Correlators of Large-N Fermionic Chern-Simons Vector Models, JHEP 02 (2013) 150 [arXiv:1211.1866] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    J. Maldacena and A. Zhiboedov, Constraining Conformal Field Theories with A Higher Spin Symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].ADSMathSciNetGoogle Scholar
  9. [9]
    S. Giombi and X. Yin, On Higher Spin Gauge Theory and the Critical O(N ) Model, Phys. Rev. D 85 (2012) 086005 [arXiv:1105.4011] [INSPIRE].ADSGoogle Scholar
  10. [10]
    S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    T. Takimi, Duality and higher temperature phases of large-N Chern-Simons matter theories on S2 × S1, JHEP 07 (2013) 177 [arXiv:1304.3725] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    S. Jain, S. Minwalla, T. Sharma, T. Takimi, S.R. Wadia et al., Phases of large-N vector Chern-Simons theories on S2 × S1, JHEP 09 (2013) 009 [arXiv:1301.6169] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    S. Yokoyama, Chern-Simons-Fermion Vector Model with Chemical Potential, JHEP 01 (2013) 052 [arXiv:1210.4109] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    S. Banerjee, S. Hellerman, J. Maltz and S.H. Shenker, Light States in Chern-Simons Theory Coupled to Fundamental Matter, JHEP 03 (2013) 097 [arXiv:1207.4195] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  16. [16]
    G. ’t Hooft, A Two-Dimensional Model for Mesons, Nucl. Phys. B 75 (1974) 461 [INSPIRE].ADSMathSciNetGoogle Scholar
  17. [17]
    Y. Frishman and J. Sonnenschein, Non-perturbative Field Theory, from two dimensional conformal field theory to QCD in four dimensions, Cambridge monographs on mathematical physics, Cambridge University Press, Cambridge U.K. (2010).Google Scholar
  18. [18]
    S. Jain, M. Mandlik, S. Minwalla, T. Takimi, S.R. Wadia et al., Unitarity, Crossing Symmetry and Duality of the S-matrix in large-N Chern-Simons theories with fundamental matter, arXiv:1404.6373 [INSPIRE].
  19. [19]
    W.A. Bardeen, The Massive Fermion Phase for the U(N ) Chern-Simons Gauge Theory in D=3 at Large N, JHEP 10 (2014) 039 [arXiv:1404.7477] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of Particle Physics and AstrophysicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.The Raymond and Beverly Sackler School of Physics and AstronomyTel Aviv UniversityRamat AvivIsrael

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