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

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.Comment: 19 pages LaTe

Beta-gamma systems and the deformations of the BRST operator

We describe the relation between simple logarithmic CFTs associated with closed and open strings, and their "infinite metric" limits, corresponding to the beta-gamma systems. This relation is studied on the level of the BRST complex: we show that the consideration of metric as a perturbation leads to a certain deformation of the algebraic operations of the Lian-Zuckerman type on the vertex algebra, associated with the beta-gamma systems. The Maurer-Cartan equations corresponding to this deformed structure in the quasiclassical approximation lead to the nonlinear field equations. As an explicit example, we demonstrate, that using this construction, Yang-Mills equations can be derived. This gives rise to a nontrivial relation between the Courant-Dorfman algebroid and homotopy algebras emerging from the gauge theory. We also discuss possible algebraic approach to the study of beta-functions in sigma-models.Comment: LaTeX2e, 15 pages; minor revision, typos corrected, Journal of Physics A, in pres

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

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