Cubic interactions of Maxwell-like higher spins

TL;DR

The paper develops a universal framework for cubic interactions of Maxwell-like massless higher-spin fields in flat and (A)dS spaces. By adapting the Noether procedure to constrained gauge symmetries and allowing deformations of the transversality condition, it constructs complete off-shell cubic vertices starting from the TT sector and adding divergence-based counterterms, with generalization to partially reducible and trace-containing spectra. The authors extend the construction to (A)dS using ambient space methods, derive AdS-specific vertex structures, and illustrate concrete reductions (e.g., the 4-0-0 case) and off-shell generating functions with Grassmann variables. These results suggest a simpler yet flexible route to higher-spin interactions across diverse spectra and hint at connections to tensionless strings and holography, while outlining challenges for quartic and global consistency.

Abstract

We study the cubic vertices for Maxwell-like higher-spins in flat and (A)dS background spaces of any dimension. Reducibility of their free spectra implies that a single cubic vertex involving any three fields subsumes a number of couplings among different particles of various spins. The resulting vertices do not involve traces of the fields and in this sense are simpler than their Fronsdal counterparts. We propose an extension of both the free theory and of its cubic deformation to a more general class of partially reducible systems, that one can obtain from the original theory upon imposing trace constraints of various orders. The key to our results is a version of the Noether procedure allowing to systematically account for the deformations of the transversality conditions to be imposed on the gauge parameters at the free level.

Figures (2)

• Figure 1: Maxwell-like decomposition of the stringy massless spectrum of generalised Vasiliev theory with symmetry algebra $U(\infty)\otimes Vas_d$ . $N$ numerates Regge trajectories, starting with the trajectory $N=0$. Blue dots with coordinates $(s,n)$ correspond to massless states of spin $s$ in $n$-th "Regge trajectory", while the lines connect the particles that combine into reducible representation described by Maxwell-like field.
• Figure 2: Maxwell-like decomposition of the spectrum of generalized Vasiliev theory with four Regge trajectories and symmetry algebra $U(2)\otimes Vas_d$ . Blue dots with coordinates $(s,n)$ correspond to massless states of spin $s$ in $n$-th "Regge trajectory", while the lines connect the particles that combine into reducible representation described by Maxwell-like field with fourth trace constraint.