Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators

TL;DR

This paper develops a systematic method to relate correlation functions in Large N Slightly Broken Higher Spin theories to free theory correlators, revealing simple forms and interpolations between free fermionic and bosonic theories, and manifesting 3D bosonization.

Contribution

It introduces a systematic approach to constrain and compute n-point functions in SBHS theories, connecting them to free theory correlators and demonstrating 3D bosonization.

Findings

Correlation functions in SBHS theories are simple and relate to free fermionic and bosonic correlators.

The method reproduces known three-point functions and extends to four and higher points.

An anyonic phase interpolates between free fermionic and bosonic results, making 3D bosonization explicit.

Abstract

We develop a systematic method to constrain any n-point correlation function of spinning operators in Large N Slightly Broken Higher Spin (SBHS) theories. As an illustration of the methodology, we work out the three point functions which reproduce the previously known results. We then work out the four point functions of spinning operators. We show that the correlation functions of spinning operators in the interacting SBHS theory take a remarkably simple form and that they can be written just in terms of the free fermionic and critical bosonic theory correlators. They also interpolate nicely between the results in these two theories. When expressed in spinor-helicity variables we obtain an anyonic phase which nicely interpolates between the free fermionic and critical bosonic results which makes 3D bosonization manifest. Further, we also obtain a form for five and higher point functions as well by performing a similar analysis.