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d = 3 bosonic vector models coupled to Chern-Simons gauge theories

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Abstract

We study three dimensional O(N) k and U(N) k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is conjectured to be dual to Vasiliev’s higher spin gravity theory on AdS 4. For large k and N we obtain a parity-breaking deformation of this theory, controlled by the ’t Hooft coupling λ = 4πN/k. For infinite N we argue (and show explicitly at two-loop order) that the theories with finite λ are conformally invariant, and also have an exactly marginal (ϕ 2)3 deformation. For large but finite N and small ’t Hooft coupling λ, we show that there is still a line of fixed points parameterized by the ’t Hooft coupling λ. We show that, at infinite N, the interacting non-parity-invariant theory with finite λ has the same spectrum of primary operators as the free theory, consisting of an infinite tower of conserved higher-spin currents and a scalar operator with scaling dimension Δ = 1; however, the correlation functions of these operators do depend on λ. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by λ, and continuously connected to Vasiliev’s theory. For finite N the higher spin currents are not conserved.

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Authors and Affiliations

  1. Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, 76100, Israel

    Ofer Aharony, Guy Gur-Ari & Ran Yacoby

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  1. Ofer Aharony
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  2. Guy Gur-Ari
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  3. Ran Yacoby
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Correspondence to Ofer Aharony.

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ArXiv ePrint: 1110.4382

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Aharony, O., Gur-Ari, G. & Yacoby, R. d = 3 bosonic vector models coupled to Chern-Simons gauge theories. J. High Energ. Phys. 2012, 37 (2012). https://doi.org/10.1007/JHEP03(2012)037

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