A Spin on the Bulk Locality of Slightly Broken Higher Spin Theories

TL;DR

This paper explores the expression of correlation functions in large N Chern-Simons matter theories using twist conformal blocks, revealing that exact higher spin symmetry allows such expressions, but slight breaking complicates this.

Contribution

Develops methods for spinning twist conformal blocks and analyzes their role in correlators of higher spin theories, highlighting differences between exact and broken symmetry cases.

Findings

Spinning correlators with exact higher spin symmetry can be expressed in terms of single trace TCBs.

Slight breaking of higher spin symmetry prevents general spinning correlators from being expressed solely in terms of TCBs.

Potential identification of a local bulk dual sector within SBHS theories.

Abstract

In this paper, we investigate if it is possible to express correlation functions in Large N Chern-Simons (CS) matter theories/ Slightly Broken Higher Spin (SBHS) theories purely in terms of single trace twist conformal blocks (TCBs). For this, we first develop the machinery for spinning TCBs. We do this both by explicitly solving the spinning TCB eigenvalue equation taking into account consistency with the operator product expansion (OPE) and crossing symmetry, and also by employing weight shifting and spin raising operators and acting with them on scalar seeds. Using these results we show that spinning correlators in theories with exact higher spin symmetry can be entirely expressed in terms of single trace TCBs. However, when the higher spin symmetry is slightly broken at large- N, even though the scalar four-point function is given by single-trace TCBs, the spinning correlators in general, are not. Our results suggest that it may be possible to identify a sub-sector of SBHS theory which has a local bulk dual.