# Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations

## TL;DR

This paper derives the form of higher-spin current interactions in the one-form sector from nonlinear higher-spin equations in AdS4, revealing phase independence and explicit spin-dependent couplings, confirming a key conjecture about self-dual sectors.

## Contribution

It provides a detailed derivation of current interactions from nonlinear higher-spin equations, showing phase independence and explicit coupling constants, advancing understanding of higher-spin gauge theories.

## Key findings

- Quadratic corrections are phase-independent.
- Current interactions are expressed in minimal derivative form.
- Spin-dependent couplings are explicitly determined.

## Abstract

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in $AdS_4$. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter $\eta =\exp i\varphi$ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant $\eta\bar\eta$. Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at ($\eta=0$) $\bar \eta=0$.