Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization

Abstract

Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the planar four-point functions at arbitrary ’t Hooft coupling λ in the CFTs with slightly broken higher spin symmetry. We use a bootstrap approach based on the approximate higher spin Ward identity. We show that the bootstrap equation is separated into two parts with opposite parity charges, and it leads to a recursion relation for the λ expansions of the correlation functions. The λ expansions terminate at order λ2 and the solutions are exact in λ. Our work generalizes the approach proposed by Maldacena and Zhiboedov to four-point correlators, and it amounts to an on-shell study for the 3D Chern-Simons vector models and their holographic duals in AdS4. Besides, we show that the same results can also be obtained rather simply from bosonization duality of 3D Chern-Simons vector models. The odd term at order O(λ) in the spinning four-point function relates to the free boson correlator through a Legendre transformation. This provides new evidence on the 3D bosonization duality at the spinning four-point function level. We expect this work can be generalized to a complete classification of general four-point functions of single trace currents.