Conformal Killing Tensors, Noether Currents and Higher-Spin Shift Symmetries in (A)dS Space

TL;DR

This paper explores the relationship between shift symmetries, conserved currents, and conformal Killing tensors in higher-spin fields on (A)dS space, revealing a one-to-one correspondence between two seemingly different sets of conserved quantities.

Contribution

It proves that the two sets of conserved currents associated with shift symmetries and conformal Killing tensors are equivalent, clarifying their relationship in higher-spin theories on (A)dS.

Findings

Two sets of conserved currents are shown to be equivalent.

Each conformal Killing tensor corresponds to a unique shift symmetry.

The correspondence holds across all relevant mass values and spins.

Abstract

For certain mass values, shift symmetries appear among massive higher spin fields propagating on (anti-) de Sitter spacetime. On the one hand, Noether's theorem assigns a set of conserved currents for each shift symmetric field, one current for each of the independent shift symmetries. On the other hand, each shift symmetric field comes with a higher-rank conserved field strength that can be contracted with a conformal Killing tensor (CKT) to form another set of conserved currents, one for each independent CKT. This second set is naively much larger than the first. We conjecture, and prove in the first few cases, that these two sets are the same once we account for the redundancy due to trivial currents that is implicit in Noether's theorem. For each field, only one branch of the CKTs is non-trivial. As we range over all the mass values and spins of the shift symmetric fields, each kind of CKT gets used exactly once in a non-trivial current.