Electromagnetic Interactions of Massive Higher-Spin Fields in 3D via Chiral Theory

TL;DR

This paper develops a novel framework for describing electromagnetic interactions of massive higher-spin fields in 3D, utilizing dimensional reduction from chiral higher-spin theories, resulting in non-minimal interactions with specific gyromagnetic ratios.

Contribution

It introduces a new approach to higher-spin field interactions in 3D by deriving consistent equations from higher-dimensional chiral theories, including a new Lagrangian for free massive higher-spin fields.

Findings

Electromagnetic fields satisfy the Bogomolny equation.

Interaction is non-minimal with gyromagnetic ratio g=1/s.

Derived a new Lagrangian for free massive higher-spin fields.

Abstract

We address the issue of electromagnetic interaction for massive higher-spin fields in $3d$ Minkowski space. We show that consistent field equations can be obtained through the dimensional reduction of the higher-spin extension of self-dual Yang-Mills theory, which itself is a truncation of chiral higher-spin gravity in four dimensions. The resulting electromagnetic field satisfies the Bogomolny equation, and the interaction is non-minimal with the gyromagnetic ratio given by $g=1/s$, where $s$ is the spin. As a by-product, we obtain a new Lagrangian for free massive higher-spin fields in $3d$.