Local Interactions of Higher-Spin Potentials That are Gauge Invariant in Linear Approximation

TL;DR

This paper investigates the structure of gauge-invariant, linearized higher-spin interactions derived from conserved currents in scalar field theories, focusing on their regularization and local interaction properties.

Contribution

It introduces a method to compute the residue of UV divergences in higher-spin current interactions, revealing their gauge invariance and locality in the linear approximation.

Findings

Residue of UV divergence yields a local, gauge-invariant interaction Lagrangian

Method applies to connected Wightman functions of conserved currents

Supports the construction of consistent higher-spin gauge theories

Abstract

We study connected Wightman functions of $N$ conserved currents, each of which is formed from a scalar field and has even spin $l_{i}$. The UV divergence of this vertex function is regularized by the analytic continuation in the space dimension $D\longrightarrow D-\epsilon$. We evaluate the residue of $\epsilon ^{-1}$ only, which is a local interaction Lagrangian density and gauge invariant in linear