Generating functions of (partially-)massless higher-spin cubic interactions

TL;DR

This paper develops generating functions for cubic interactions of (partially-)massless higher-spin fields in (A)dS space, revealing conditions under which the number of consistent couplings increases and identifying solutions that lead to non-Abelian gauge symmetry deformations.

Contribution

It provides explicit solutions to the differential equations governing higher-spin interactions and highlights the special mass conditions enabling non-Abelian gauge deformations in (A)dS space.

Findings

Number of consistent couplings increases at specific mass values.

Only certain solutions lead to non-Abelian gauge symmetry deformations.

Distinctive mass conditions in (A)dS space compared to flat space.

Abstract

Generating functions encoding cubic interactions of (partially-)massless higher-spin fields are provided within the ambient-space formalism. They satisfy a system of higher-order partial differential equations that can be explicitly solved due to their factorized form. We find that the number of consistent couplings increases whenever the squares of the field masses take some integer values (in units of the cosmological constant) and satisfy certain conditions. Moreover, it is shown that only the supplemental solutions can give rise to non-Abelian deformations of the gauge symmetries. The presence of these conditions on the masses is a distinctive feature of (A)dS interactions that has in general no direct counterpart in flat space.