Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra

TL;DR

This paper investigates the spectrum and symmetry algebra of conformal higher-spin gravity, proposing a regularization method that reveals an equality of characters and a rearrangement of degrees of freedom.

Contribution

It introduces a regularization technique for divergent sums in the spectrum and symmetry characters, confirming their equality in type-A and type-B theories.

Findings

Characters of the spectrum and symmetry algebra are equal after regularization

Regularization confirms a rearrangement of degrees of freedom in conformal higher-spin gravity

Results apply to type-A, type-B, and higher-depth theories

Abstract

The linearized spectrum and the algebra of global symmetries of conformal higher-spin gravity decompose into infinitely many representations of the conformal algebra. Their characters involve divergent sums over spins. We propose a suitable regularization adapted to their evaluation and observe that their characters are actually equal. This result holds in the case of type-A and type-B (and their higher-depth generalizations) theories and confirms previous observations on a remarkable rearrangement of dynamical degrees of freedom in conformal higher-spin gravity after regularization.