Four point functions in CFT's with slightly broken higher spin symmetry

TL;DR

This paper calculates spinning four-point functions in a 3D conformal field theory with slightly broken higher spin symmetry, using Mellin space ansatz and crossing symmetry to fix coefficients, with potential for broader application.

Contribution

It introduces a novel method to compute spinning four-point functions in quasi-fermionic 3D CFTs with broken higher spin symmetry using Mellin space techniques.

Findings

Derived a formula for four-point functions involving higher spin currents and scalars.

Developed a systematic approach using Mellin space and crossing symmetry.

Method can be extended to compute all spinning four-point functions in these theories.

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 $\langle j_s j_{\tilde{0}} j_{\tilde{0}} j_{\tilde{0}} \rangle$, where $j_s$ 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.