Spontaneous Breaking of Scale Invariance in a d=3 U(N) Model with Chern-Simons Gauge Field

Abstract

We study spontaneous breaking of scale invariance in the large N limit of three dimensional $U(N{)}_{\kappa }$ Chern-Simons theories coupled to a scalar field in the fundamental representation. When a ${\lambda }_6({\varphi }^{†}\cdot \varphi {)}^3$ self interaction term is added to the action we find a massive phase at a certain critical value for a combination of the ${\lambda }_6$ and 't Hooft's $\lambda =N/\kappa$ couplings. This model attracted recent attention since at finite $\kappa$ it contains a singlet sector which is conjectured to be dual to Vasiliev's higher spin gravity on $Ad{S}_4$. 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.

23 pages, 8 figures. several lines changed in the introduction. typos corrected

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