Abstract
We explore the phase structure of fermions in the U(N) Chern-Simons Gauge theory in three dimensions using the large N limit where N is the number of colors and the fermions are taken to be in the fundamental representation of the U(N) gauge group. In the large N limit, the theory retains its classical conformal behavior and considerable attention has been paid to possible AdS/CFT dualities of the theory in the conformal phase. In this paper we present a solution for the massive phase of the fermion theory that is exact to the leading order of ‘t Hooft’s large N expansion. We present evidence for the spontaneous breaking of the exact scale symmetry and analyze the properties of the dilaton that appears as the Goldstone boson of scale symmetry breaking.
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References
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
M. Moshe and J. Zinn-Justin, Quantum field theory in the large-N limit: A Review, Phys. Rept. 385 (2003) 69 [hep-th/0306133] [INSPIRE].
S. Giombi et al., Chern-Simons Theory with Vector Fermion Matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
S. Giombi, S. Prakash and X. Yin, A Note on CFT Correlators in Three Dimensions, JHEP 07 (2013) 105 [arXiv:1104.4317] [INSPIRE].
S. Jain, S.P. Trivedi, S.R. Wadia and S. Yokoyama, Supersymmetric Chern-Simons Theories with Vector Matter, JHEP 10 (2012) 194 [arXiv:1207.4750] [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].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, hep-th/9910096 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B 189 (1987) 89 [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 Spins in AdS and Twistorial Holography, JHEP 04 (2011) 086 [arXiv:1004.3736] [INSPIRE].
S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
W.A. Bardeen and M. Moshe, Spontaneous breaking of scale invariance in a D =3 U(N ) model with Chern-Simons gauge fields, JHEP 06 (2014) 113 [arXiv:1402.4196] [INSPIRE].
W.A. Bardeen, M. Moshe and M. Bander, Spontaneous Breaking of Scale Invariance and the Ultraviolet Fixed Point in O(n) Symmetric (phi 6 in Three-Dimensions) Theory, Phys. Rev. Lett. 52 (1984) 1188 [INSPIRE].
W.A. Bardeen, K. Higashijima and M. Moshe, Spontaneous Breaking of Scale Invariance in a Supersymmetric Model, Nucl. Phys. B 250 (1985) 437 [INSPIRE].
M. Moshe and J. Zinn-Justin, private communication.
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ArXiv ePrint: 1404.7477
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Bardeen, W.A. The massive fermion phase for the U(N) Chern-Simons gauge theory in D=3 at large N. J. High Energ. Phys. 2014, 39 (2014). https://doi.org/10.1007/JHEP10(2014)039
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DOI: https://doi.org/10.1007/JHEP10(2014)039