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

Kurt Hinterbichler, Samanta Saha, Thomas Yan

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.

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

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.
Paper Structure (6 sections, 46 equations, 1 figure)

This paper contains 6 sections, 46 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Conformal Killing Tensors on dS$_D$
  3. Noether Currents
  4. Correspondence
  5. Examples
  6. Acknowledgments:

Figures (1)

  • Figure 1: Matching of non-trivial currents to shift symmetries. Each red dot represents a different Killing tensor mode. The various lines indicate $r,l$ values of the Killing tensor mode, as well as the $s,k$ values of the shift symmetric field for which it occurs non-trivially.