CFT correlators from slightly broken higher spin symmetry

Abstract

Conformal invariance completely fixes the form of 2- and 3-point functions in a conformal field theory (CFT). However, this does not extend to higher point functions where the correlator is only determined up to arbitrary functions of cross-ratios. In this thesis, we study three-dimensional CFTs with an infinite tower of higher-spin currents such as the bosonic and fermionic theories coupled to Chern-Simons gauge field. Computing 4-point correlators in these theories is technically and conceptually difficult. Here we make use of the additional higher spin symmetries to obtain 2- and 3- point correlators in these theories. The method involved uses slightly broken higher spin equations and spinor helicity variables which help compute 4-point interacting theory correlators in terms of free theory results. We further propose a modification of the symmetry algebra that predicts a possible form of an e↵ective current in the theory.