# On current contribution to Fronsdal equations

## TL;DR

This paper derives explicit quadratic corrections to bosonic Fronsdal equations from a local form of Vasiliev equations, confirming the consistency of proposed field redefinitions and matching known cubic vertex expressions.

## Contribution

It provides explicit quadratic corrections to Fronsdal equations from Vasiliev's local second-order equations, supporting the proposed field redefinition and extending previous results.

## Key findings

- Quadratic corrections match known cubic vertices in parity-invariant case
- Explicit expressions derived for general phase factors
- Supports the validity of the proposed field redefinition

## Abstract

We explore a local form of second-order Vasiliev equations proposed in [arXiv:1706.03718] and obtain an explicit expression for quadratic corrections to bosonic Fronsdal equations, generated by gauge-invariant higher-spin currents. Our analysis is performed for general phase factor, and for the case of parity-invariant theory we find the agreement with expressions for cubic vertices available in the literature. This provides an additional indication that field redefinition proposed in [arXiv:1706.03718] is the proper one.