Mixed-symmetry multiplets and higher-spin curvatures

TL;DR

This paper investigates higher-derivative equations for mixed-symmetry gauge potentials, demonstrating their equivalence to known second-order equations and clarifying their particle content and algebraic structure.

Contribution

It introduces a unified analysis of higher-derivative curvature equations for mixed-symmetry fields and relates them to existing second-order formulations, including a simplified Ricci-like case.

Findings

Higher-derivative equations propagate the same multiplets as second-order equations.

The Ricci-like case with trace conditions is explicitly characterized.

Particle content is algebraically evaluated for different formulations.

Abstract

We study the higher-derivative equations for gauge potentials of arbitrary mixed-symmetry type obtained by setting to zero the divergences of the corresponding curvature tensors. We show that they propagate the same reducible multiplets as the Maxwell-like second-order equations for gauge fields subject to constrained gauge transformations. As an additional output of our analysis, we provide a streamlined presentation of the Ricci-like case, where the traces of the same curvature tensors are set to zero, and we present a simple algebraic evaluation of the particle content associated with the Labastida and with the Maxwell-like second-order equations.