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

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.

19 pages LaTeX

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Cited by in corpus (11)

• Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space
• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Tractors, Mass and Weyl Invariance
• Weyl Invariance and the Origins of Mass
• Gravitational and higher-derivative interactions of massive spin 5/2 field in (A)dS space
• Conformal Field Theory and Algebraic Structure of Gauge Theory
• Detours and Paths: BRST Complexes and Worldline Formalism
• BRST Detour Quantization
• Metric projective geometry, BGG detour complexes and partially massless gauge theories
• Homotopy Algebras of Differential (Super)forms in Three and Four Dimensions
• Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes