A Talk on 3d Matter Coupled to Chern-Simons Field, Spontaneous Breaking of Scale Invariance, and Fermion-Boson Mapping

The singlet sector of vector, large $N$, 3d field theory corresponds to Vasiliev higher spin theory on $Ad{S}_4$. Will discuss three dimensional $U(N)$ symmetric field theory with fermion and boson matter coupled to a topological Chern-Simons field. In the presence of a marginal deformation will determine the conditions for the existence of a phase with spontaneous breaking of scale invariance. In this phase the ground state contains massive $U(N)$ quanta and a massless $U(N)$ singlet bound state goldstone boson:~the Dilaton. Will show that such a phase appears only in the presence of a marginal deformation. The massless Dilaton appears in the spectrum provided certain relations between coupling constants are satisfied. Will discuss the fermion-boson mapping and show that the conditions for spontaneous breaking of scale invariance in the boson and fermion theories are copies of each other.