# Test of the local form of higher-spin equations via AdS/CFT

## TL;DR

This paper tests the local form of higher-spin equations within the AdS/CFT framework, confirming their consistency with correlators and discussing necessary modifications for parity-broken models.

## Contribution

It demonstrates the validity of the local higher-spin equations in reproducing AdS/CFT correlators and explores modifications needed for parity-breaking boundary conditions.

## Key findings

- Local higher-spin equations reproduce expected AdS/CFT correlators.
- Parity-broken models require modified boundary conditions and doubled fields.
- Nonlinear deformations are necessary for higher-order consistency.

## Abstract

The local form of higher-spin equations found recently to the second order [1] is shown to properly reproduce the anticipated $AdS/CFT$ correlators for appropriate boundary conditions. It is argued that consistent $AdS/CFT$ holography for the parity-broken boundary models needs a nontrivial modification of the bosonic truncation of the original higher-spin theory with the doubled number of fields, as well as a nonlinear deformation of the boundary conditions in the higher orders.