Higher-spin helicities from characteristic-form descent

Determine whether the higher-spin quadratic helicities can be obtained from the descent of genuine higher-spin characteristic forms, particularly for metric-like higher-spin fields whose generalized curvatures do not automatically define ordinary differential-form characteristic classes.

Background

The paper constructs parity-odd quadratic helicity functionals for the spin-1 and spin-2 sectors of linearized gravity by reducing the Nieh–Yan and Pontryagin terms to spacelike hypersurfaces. It then proposes a broader hierarchy for symmetric, transverse, and traceless massless fields of arbitrary integer spin, using a generalized symmetric curl and powers of the spatial Laplacian.

The authors emphasize that, for higher-spin fields, the Pauli–Lubanski construction specifies the helicity operator and spectrum but does not by itself determine the normalization, conservation law, boundary completion, or topological origin of the associated quadratic functionals. The unresolved issue is whether these functionals admit an origin analogous to the characteristic-class descent available for ordinary gauge connections.