Abstract
We analyze the theory of massive fermions in the fundamental representation coupled to a U(N) Chern-Simons gauge theory at level K. It is done in the large N, large K limits where λ = \( \frac{N}{K} \) is kept fixed. Following [1] we obtain the solution of a Schwinger-Dyson equation for the two point function, the exact expression for the fermion propagator and the partition function at finite temperature. We prove that in the large K limit there exists an infinite set of classically conserved high spin currents also when a mass is introduced, breaking the conformal invariance. In analogy to the seminal work of ’t Hooft on two dimensional QCD, we write down a Bethe-Salpeter equation for the wave function of a “quark anti-quark” bound state. We show that unlike the two dimensional QCD case, the three dimensional Chern-Simons theory does not admit a confining spectrum.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Giombi et al., Chern-Simons theory with vector fermion matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
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].
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].
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].
G. Gur-Ari and R. Yacoby, Correlators of large-N fermionic Chern-Simons vector models, JHEP 02 (2013) 150 [arXiv:1211.1866] [INSPIRE].
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].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a higher spin symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
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].
S. Giombi and X. Yin, Higher spin gauge theory and holography: the three-point functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
T. Takimi, Duality and higher temperature phases of large-N Chern-Simons Matter theories on S 2 × S 1, arXiv:1304.3725 [INSPIRE].
S. Jain et al., Phases of large-N vector Chern-Simons theories on S 2 × S 1, JHEP 09 (2013) 009 [arXiv:1301.6169] [INSPIRE].
S. Yokoyama, Chern-Simons-fermion vector model with chemical potential, JHEP 01 (2013) 052 [arXiv:1210.4109] [INSPIRE].
S. Giombi and X. Yin, The higher spin/vector model duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
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].
G. ’t Hooft, A two-dimensional model for mesons, Nucl. Phys. B 75 (1974) 461 [INSPIRE].
C.G. Callan Jr., N. Coote and D.J. Gross, Two-dimensional Yang-Mills theory: a model of quark confinement, Phys. Rev. D 13 (1976) 1649 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1306.6465
Rights and permissions
About this article
Cite this article
Frishman, Y., Sonnenschein, J. Breaking conformal invariance — Large N Chern-Simons theory coupled to massive fundamental fermions. J. High Energ. Phys. 2013, 91 (2013). https://doi.org/10.1007/JHEP12(2013)091
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2013)091