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The singlet sector of vector, large $N$, 3d field theory corresponds toVasiliev higher spin theory on $AdS_4$. Will discuss three dimensional $U(N)$symmetric field theory with fermion and boson matter coupled to a topologicalChern-Simons field. In the presence of a marginal deformation will determinethe conditions for the existence of a phase with spontaneous breaking of scaleinvariance. In this phase the ground state contains massive $U(N)$ quanta and amassless $U(N)$ singlet bound state goldstone boson:~the Dilaton. Will showthat such a phase appears only in the presence of a marginal deformation. Themassless Dilaton appears in the spectrum provided certain relations betweencoupling constants are satisfied. Will discuss the fermion-boson mapping andshow that the conditions for spontaneous breaking of scale invariance in theboson and fermion theories are copies of each other.

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