Slightly Broken Higher Spin Symmetry: General Structure of Correlators

We explore a class of CFT's with higher spin currents and charges. Away from the free or $N=\infty$ limit the non-conservation of currents is governed by operators built out of the currents themselves, which deforms the algebra of charges by, and together with, its action on the currents. This structure is encoded in a certain $A_\infty/L_\infty$-algebra. Under quite general assumptions we construct invariants of the deformed higher spin symmetry, which are candidate correlation functions. In particular, we show that there is a finite number of independent structures at the $n$-point level. The invariants are found to have a form reminiscent of a one-loop exact theory. In the case of Chern--Simons vector models the uniqueness of the invariants implies the three-dimensional bosonization duality in the large-$N$ limit.