High Energy Theory Seminar

I will review the recent progress in the study of three dimensional U(N)_k Chern-Simons theories coupled to a massless boson or fermion in the fundamental representation. In particular, in the planar limit, one can determine the conformal fixed points and spectrum of local primary operators of these theories. In addition, the planar 3-point functions can be computed exactly as a function of the 't Hooft coupling, and the results agree with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have high-spin symmetries in the large N limit. It has been suggested in the past that the fermionic and bosonic theories are dual to each other at large N. Using the exact expressions of the planar 3-point functions, one can find the precise mapping between the two theories. In particular, it was found that the theory of N scalars coupled to a U(N)_k Chern-Simons theory is equivalent to the Gross-Neveu model of k fermions coupled to a U(k)_N Chern-Simons theory, thus providing a bosonization of the latter theory.