Exact higher-spin symmetry in CFT: free fermion correlators from Vasiliev Theory

TL;DR

The paper shows that exact higher-spin symmetry in AdS_4/CFT_3 fixes the connected correlators of conserved currents and the weight-two scalar in the 3d free-fermion CFT by using Vasiliev's HS theory. It extends previous HS-based boundary calculations by incorporating the Δ=2 scalar operator \tilde{j}_0 and providing explicit generating-function techniques that yield two-, three-, and four-point functions in terms of HS-invariant conformal structures P, Q, and a new R, with a θ-parameter interpolating between free boson and free fermion results. The main contribution is a bulk-derived, HS-covariant framework that reproduces known results and connects neatly to boundary operator algebras, matching Maldacena–Zhiboedov and Gelfond–Vasiliev findings. This approach yields compact, symmetry-driven expressions for n-point correlators and offers a path to generalizations to other dimensions and to cases with HS breaking.

Abstract

N-point correlation functions of conserved currents and weight-two scalar operators of the three-dimensional free fermion vector model are found as invariants of the higher-spin symmetry in four-dimensional AdS. These are the correlators of the unbroken Vasiliev higher-spin theory. The results extend the recent work arXiv:1210.7963 and are complementary to arXiv:1301.3123 where the correlators were computed entirely on the boundary.