Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra

Understand

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.