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

Understand

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 $\lambda_6(\phi^\dagger\cdot\phi)^3$ 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 $AdS_4$.
• Our paper concentrates on the massive phase of the 3d boundary theory.