Abstract
We study spontaneous breaking of scale invariance in the large N limit of three dimensional U(N ) κ Chern-Simons theories coupled to a scalar field in the fundamental representation. When a λ6(ϕ † · ϕ)3 self interaction term is added to the action we find a massive phase at a certain critical value for a combination of the λ6 and ’t Hooft’s λ = N/κ couplings. This model attracted recent attention since at finite κ it contains a singlet sector which is conjectured to be dual to Vasiliev’s higher spin gravity on AdS 4. Our paper concentrates on the massive phase of the 3d boundary theory. We discuss the advantage of introducing masses in the boundary theory through spontaneous breaking of scale invariance.
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References
B. Sundborg, Stringy gravity, interacting tensionless strings and massless higher spins, Nucl. Phys. Proc. Suppl. 102 (2001) 113 [hep-th/0103247] [INSPIRE].
E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. B 660 (2003) 403] [hep-th/0205131] [INSPIRE].
E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N ) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: star product and AdS space, in The many faces of the superworld, M.A. Shifman ed., World Scientific, Singapore (1999), pg. 533 [hep-th/9910096] [INSPIRE].
S. Giombi and X. Yin, Higher spin gauge theory and holography: the three-point functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [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, On higher spin gauge theory and the critical O(N ) model, Phys. Rev. D 85 (2012) 086005 [arXiv:1105.4011] [INSPIRE].
S. Giombi, S. Prakash and X. Yin, A note on CFT correlators in three dimensions, JHEP 07 (2013) 105 [arXiv:1104.4317] [INSPIRE].
R. de Mello Koch, A. Jevicki, K. Jin and J.P. Rodrigues, AdS 4 /CFT 3 construction from collective fields, Phys. Rev. D 83 (2011) 025006 [arXiv:1008.0633] [INSPIRE].
R. de Mello Koch, A. Jevicki, K. Jin, J.P. Rodrigues and Q. Ye, S = 1 in O(N )/HS duality, Class. Quant. Grav. 30 (2013) 104005 [arXiv:1205.4117] [INSPIRE].
M.R. Douglas, L. Mazzucato and S.S. Razamat, Holographic dual of free field theory, Phys. Rev. D 83 (2011) 071701 [arXiv:1011.4926] [INSPIRE].
S. Giombi et al., Chern-Simons theory with vector fermion matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [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].
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, 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, 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].
C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ triality: from higher spin fields to strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [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].
W.A. Bardeen, M. Moshe and M. Bander, Spontaneous breaking of scale invariance and the ultraviolet fixed point in O(N ) symmetric ϕ 6 in three-dimensions theory, Phys. Rev. Lett. 52 (1984) 1188 [INSPIRE].
D.J. Amit and E. Rabinovici, Breaking of scale invariance in ϕ 6 theory: tricriticality and critical end points, Nucl. Phys. B 257 (1985) 371 [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].
J. Feinberg, M. Moshe, M. Smolkin and J. Zinn-Justin, Spontaneous breaking of scale invariance and supersymmetric models at finite temperature, Int. J. Mod. Phys. A 20 (2005) 4475 [INSPIRE].
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Bardeen, W.A., Moshe, M. Spontaneous breaking of scale invariance in a D = 3 U(N ) model with Chern-Simons gauge fields. J. High Energ. Phys. 2014, 113 (2014). https://doi.org/10.1007/JHEP06(2014)113
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DOI: https://doi.org/10.1007/JHEP06(2014)113