Higher Spin Gravitational Couplings and the Yang--Mills Detour Complex

TL;DR

This paper introduces a new framework for consistent higher spin gravitational couplings using a Yang--Mills detour complex, revealing a rich spectrum with both physical and ghost-like excitations, relevant for advanced theoretical models.

Contribution

It presents the first example of a Yang--Mills detour complex applied to higher spin gravity, enabling consistent coupling to various gravitational backgrounds at the classical level.

Findings

Identifies a spectrum with a massless graviton, scalar, and massive vector

Discovers negative norm excitations and non-unitary evolution in coherent states

Highlights relevance for braneworld and ghost condensation models

Abstract

Gravitational interactions of higher spin fields are generically plagued by inconsistencies. We present a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang--Mills detour complex, which recently has been applied in the mathematical setting of conformal geometry. An analysis of asymptotic scattering states about the trivial field theory vacuum in the simplest version of the theory yields a rich spectrum marred by negative norm excitations. The result is a theory of a physical massless graviton, scalar field, and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector of the model do have positive norms, but their evolution is no longer unitary and their amplitudes grow with time. The model is of considerable interest for braneworld scenarios and ghost condensation models, and invariant theory.