Surface charges and dynamical Killing tensors for higher spin gauge fields in constant curvature spaces

TL;DR

The paper addresses how to define and classify surface charges for massless higher-spin gauge fields in constant curvature spaces. It establishes a one-to-one correspondence between surface charges and divergence-free Killing tensors by leveraging a BRST first-quantized description of the Fronsdal theory, solving Killing-tensor equations in flat and (A)dS backgrounds, and deriving explicit conserved (n-2)-forms. The work shows that the charges are determined by standard Killing tensors independent of the dynamics in dimensions ≥3 and reduces to Abbott-Deser results for lower spins. It further connects the field-theory characteristic cohomology to the BRST cohomology of the underlying first-quantized model, with implications for higher-spin interactions in AdS and potential links to string field theory.

Abstract

In the context of massless higher spin gauge fields in constant curvature spaces, we compute the surface charges which generalize the electric charge for spin one, the color charges in Yang-Mills theories and the energy-momentum and angular momentum for asymptotically flat gravitational fields. We show that there is a one-to-one map from surface charges onto divergence free Killing tensors. These Killing tensors are computed by relating them to a cohomology group of the first quantized BRST model underlying the Fronsdal action.