Abstract
We compute spinning four point functions in the quasi-fermionic three dimensional conformal field theory with slightly broken higher spin symmetry at finite t’Hooft coupling. More concretely, we obtain a formula for leftlangle {j}_s{j}_{tilde{0}}{j}_{tilde{0}}{j}_{tilde{0}}rightrangle , where js is a higher spin current and {j}_{tilde{0}} is the scalar single trace operator. Our procedure consists in writing a plausible ansatz in Mellin space and using crossing, pseudo-conservation and Regge boundedness to fix all undetermined coefficients. Our method can potentially be generalised to compute all spinning four point functions in these theories.
Highlights
Maldacena and Zhiboedov [5], where all three point functions of single trace operators at the planar level were computed at finite t’Hooft coupling
The formulas we obtain are very simple and our formalism, which is based on pure CFT arguments in which Mellin space plays an important role, potentially paves the way for the computation of all spinning four point functions
In [5] three point functions of single trace operators were computed at the planar level and for finite λthrough the use of slightly broken higher spin Ward identities
Summary
Jsj0j0j0 is constrained by invariance under interchange of points 2 ↔ 3 and 2 ↔ 4 This crossing symmetry implies the equations p(γ12, γ14; s, k) =. Since ∂ · js is a primary operator of spin s − 1 and dimension s + 2, ∂ · jsj0j0j0 is a conformal four point function of primary operators. We checked that the short distance limit of our expression for jsj0j0j0 cb agrees with the correct three point structures for the exchange of higher spin currents. It is not legal to add them to (1.1)
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