Paper detail

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

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 $λ_6(ϕ^\dagger\cdotϕ)^3$ self interaction term is added to the action we find a massive phase at a certain critical value for a combination of the $λ_6$ 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.